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ASTRONOMY 

EXPLAINED  UPON 

SIR  ISAAC  NEWTON'S  PRINCIPLES, 

AND 

«ADE    EASY   TO    THOSE    WHO    HAVE    NOT    STUDIED   MATHEMATICS. 
TO    WHICH    ARE    ADDED, 

A  PLAIN  METHOD  OF  FINDING  THE  DISTANCES 
OF  ALL  THE  PLANETS  FROM  THE  SUN, 

BY    THE 

TRANSIT  OF  VENUS  OVER  THE  SUN'S  DISC, 
In  the  year  1761 : 

AN  ACCOUNT  OF  MR.  HORROX's  OBSERVATION 
OF  THE  TRANSIT  OF  VENUS, 

In  the  year  1639: 

~j 

AND    OF    THE 

DISTANCES  OF  ALL  THE  PLANETS  FROM  THE  SUN*, 

AS  DEDUCED  FROM  OBSERVATIONS  OF  THE  TRANSIT 
In  the  year  1761, 

BY  JAMES  FERGUSON,  F.  R.  S. 


Heb.  xi.  3.  The  worlds  were  framed  by  the  Word  of  God. 

Job  xxvi.  7.  He  liangeth  the  earth  upon  nothing. 

13.  By  his  Spirit  he  hath  garnished  the  heavens. 


THE   SECOND    AMERICAN,    FROM    THE    LAST   LONDON  EDITION 

REVISED,  CORRECTED,  AND  IMPROVED, 
BY  ROBERT  PATTERSON, 

Professor  of  Mathematics,  in  the  University  of  Pennsylvania. 


PHILADELPHIA: 

PRINTED  FOR  AND  PUBLISHED  BY  MATHEW  CAREY, 

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/*       • 


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Be  it  remembered.  That  on  the  thirteenth  day  of  February,  in  the  thirtieth 
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u  Astronomy  explained  upon  Sir  Isaac  Newton's  Principles,  and  made  easy 
to  those  who  have  not  studied  Mathematics.  To  which  are  added,  a  plain 
method  of  finding  the  distances  of  all  the  planets  from  the  sun,  by  the  transit 
of  Ven'is  over  the  sun's  disc,  in  the  year  1761 :  an  account  of  Mr.  Horrox's 
observation  of  the  transit  of  Venus,  in  the  year  1639 :  and  of  the  distances  of 
all  the  planets  from  the  sun,  as  deduced  from  observations  of  the  transit  in 
year  1761.  By  James  Ferguson,  F.  R.  S. 

Heb.  xi.  8.  The  worlds  were  framed  by  the  Word  of  God. 
Job  xxvi.  7.  H;  hangf-th  the  earth  upon  nothing. 
13,  By  his  Spirit  he  hath  garnished  the  heavens. 

The  first  American  edition,  from  the  last  London  edition;  revised,  cor- 
rected, and  improved,  by  Robert  Patterson,  Professor  of  Mathematics,  and 
Teacher  of  Natural  Philosophy,  in  the  University  of  Pennsylvania." 

In  conformity  to  the  Act  of  the  Congress  of  the  Ur-ited  States,  intituled, 
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ing, by  securing  the  Copies  of  Maps,  Charts,  and  Books,  to  the  Authors 
and  Proprietors  of  such  Copies,  during  the  Times  therein  mentioned,'  and 
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ing, historical  and  other  Prints." 

(L.  S.)  D.  CALDWELL, 

Clerk  of  the  District  of  Pennsylvania» 


F1 
/609 


PREFACE 

TO  THE  FIR3T  AMERICAN  EDITION. 


THE  well-established  reputation  of  Fergusotfs  As- 
tronomy, renders  any  particular  encomiums  on  the  work, 
at  this  time,  altogether  unnecessary. 

The  numerous  editions  through  which  this  Treatise  has 
passed,  and  the  increasing  demand  for  itf"bear  ample  testi- 
mony to  its  merit. 

The  Publisher  submits  to  the  candid  acceptance  of  his 
fellow-citizens,  this  correct  American  Edition;  for  which 
he  solicits,  and  flatters  himself  he  shall  obtain,  their  liberal 
patronage. 

No  cost  or  pains  have  been  spared  to  render  it  worthy 
of  this  patronage.  In  the  text,  a  number  of  typographi- 
cal errors,  and  grammatical  inaccuracies,  have  been  cor- 
rected ;  and  a  variety  of  notes,  explanatory  or  corrective 
of  the  text,  which  the  numerous  discoveries  since  our  au- 
thor's time  had  rendered  necessary,  have  been  occasionally 
subjoined. 

Besides,  to  this  edition  alone  there  is  prefixed  a  copious 
explanation  of  all  the  principal  terms  in  astronomy,  chro- 
nology, and  astronomical  geography,  occurring  in  the 

1 ! 


IV 

work,  arranged  in  alphabetical  order;  with  such  remarks 
and  examples  interspersed,  as  were  judged  necessary  for 
illustration :  together  with  Tables  of  the  periodical  times, 
distances,  magnitudes,  and  other  elements,  of  all  the  plan- 
ets, both  primary  and  secondary,  in  the  solar  system  ;  ac- 
cording to  the  latest  observations. 

This,  it  is  presumed,  cannot  fail  to  be  considered  as  a 
valuable  appendage  to  the  work — especially  by  the  young 
student  of  astronomy  :  as  the  glossary  will  tend  greatly  to 
facilitate  his  progress,  and  the  tables  will  present  him  with 
a  comprehensive  view  of  the  whole  science— the  result  of 
the  observations  and  researches  both  of  past  and  present 
times. 

Philadelphia,  Feb.  Utk,  1806. 


Explanation  of  the  principal  Terms  relating  to  As- 
tronomy,  Chronology \  and  the  astronomical 
parts  of  Geography  ;  with  occasional 
Illustrations  and  Remarks. 


Aberration  of  a  star,  is  a  small  apparent  motion,  occasioned 
by  a  sensible  proportior  between  the  velocity  of  light  and 
that  of  the  earth  in  its  annual  orbit.  From  this  cause, 
every  star  will,  in  the  course  of  a  year,  appear  to  describe 
a  small  ellipsis  in  the  heavens,  whose  greater  axis  =  40" 
and  its  iesser  axis,  perpendicular  to  the  ecliptic,  =  40" 
X  cos.  01  star's  -at.  (co  radius  1.)  In  astronomical  calcu- 
lations, v-'iei-fj  f  reat  accuracy  is  required,  and  the  place  of 
a  st-ir  concerned,  a  correction  on  account  of  aberration, 
as  \veil  as  oii  ether  accounts,  ou^ht  to  be  applied  to  the 
star's  place  c<s  found  in  the  tables.  This  correction  may 
r.  Lij  !>c  iG'.in.'  by  the  following  theorems ;  in  which  A  — 
the  star's  riyht  ascension,  D  =  its  declination,  and  S  =  the 
Sir,  ,de. 

.fen;  i.  ( — .1.272  cos.  (A — S))  4-  r.os.  D  -f  (0.055, 
cos,  (A  +  '">))  T-  cos.  D  =  aberr.  in  R.  A.  in  seconds  of 
time. 

Theorem  2. — 20  cos.  A.  sin.  S.  sin.  D  -f  18.346  sin. 
A.  cos.  S.  s'.n  D — 7.964  cos.  S.  cos.  D  —  aberr.  in  dec.  in 
seconds  of  u  decree  :  observing  that  the  sine,  cosine,  See. 
of  uli  arches  between  90°  and  270°  are  to  be  considered  as 
negative  i  j.nd  those  of  ail  other  arches  as  affirmative. 

a  the  stc.r  has  south  declination,  let  the  sign  of  the 
last  term  in  the  2d  theorem  be  changed. 

dc'-'-i'-itiii'm  (dkiinui)  of  a  fixed  star,  is  the  difference  be- 
:C  aiciuvcal  and  the  mean  solar  day,  which  =  3' 
6j".'j  or  c'  DO"  of  mean  time  nearly  ;  and  so  much  sooner 
vi;i  ony  fixed  star  nse,  culminate,  or  set,  every  day,  than 
on  the  pivocdins  clay  A  piaiict  is  said  to  be  accelerated 
in  iis  niO'ion,  when  its  veiocitys  in  any  part  of  its  orbit,  ex-. 
ceeds  its  mean  velocity;  and  this  wiii  always  be  the  case 
when  its  distance  from  the  Sun  is  less  than  its  mean  dis- 
tance. 


(     8     ) 

,  or  e/ioch,  any  noted  point  of  time,  in  chronology,  from 
which  events  are  reckoned,  or  computations  made.  Dif- 
ferent nations  or  people  make  use  of  different  epochs  : 
as  the  Jews,  that  of  the  creation  of  the  worjd ;  the  crris- 
tian  nations,  that  of  the  nativity  of  Christ,  A.  M.  4UC7 ; 
the  Mahometans,  that  of  the  Hegira,  or  flight  of  Maho- 
met from  Mecca,  A.  D.  622;  the  ircient  Greeks,  that  of 
the  Olympiads,  commencing  B.  C.  775  :  the  Romans,  that 
of  the  building  of  Rome,  B.  C.  752;  the  ancient  Per- 
sians and  Assyrians,  that  of  Nabonasser,  &:c. 

Altitude  of  a  celestial  body,  is  its  elevation  above  the  horizon, 
measured  on  the  arch  of  an.  azimuth-circle  intercepted  be- 
tween the  body  and  the  horizon.  The  apparent  altitude, 
or  that  measured  by  an  instrument,  re  uires  to  be  cor- 
rected in  order  to  obtain  the  true  altitude — 1.  by  subtract- 
ing the  refraction;  2.  by  adding  the  parallax;  3.  by  sub- 
tracting the  dip  corresponding  to  the  height  of  the  ob- 
server's eye  above  the  surface  of  the  earth  ;  and  4.  when 
the  lower  or  upper  limb  of  the  sun  or  moon  is  observed, 
by  adding  or  subtracting  the  apparent  semidiameter. 

Altitude,  meridian,  is  that  of  a  body  when  on  the  meridian. 

Amplitude  of  a  celestial  body,  is  an  arch  of  the  horizon  inter- 
cepted between  the  east  or  west  points  thereof,  and  that 
point  where  the  body  rises  or  sets.  The  true  amplitude 
of  a  body  may  be  found  by  the  following  proportion  : 

Racl :  cos.  lat.  :  :  sin.  dec. :  sin.  amp.  which  will  be  of 
the  same  name  (north  or  south)  with  the  declination. 

The  difference  between  the  true,  and  the  magnetic  am- 
plitude of  a  body,  or  that  observed  by  a  compass  furnished 
with  a  magnetic  needle,  will  be  the  -variation  of  the  com- 
pass. 

Angle  is  the  inclination  of  two  converging  lines  meeting  in 
a  point,  called  the  angular  point.  A  plane  angle  is  that 
-drawn  on  a  plane  surface.  The  measure  of  a  plane  angle 
is  the  arch  of  a  circle  comprehended  between  the  lines  in- 
cluding the  angle,  the  angular  point  being  the  centre.  A 
spheric 'angle  is  that  formed  by  the  intersection  of  two 
great  circles  on  the  surface  of  a  sphere.  The  measure  of 
a  spheric  angle  is  the  arch  of  a  great  circle  comprehend- 
ed between  the  two  arches  including  the  angle,  the  angu- 
lar point  being  its  pole.  A  right  angle  is  one  whose  mea- 
sure is  an  arch  of  90°.  An  acute  angle  is  one  less  than 
90°.  An  obtuse  angle,  one  greater  than  90°. 

Anomaly  is  the  angular  distance  of  a  planet  from  its  aphelion. 
It  is  distinguished  into  true,ex  centric,  and  mean.  True  ano- 
nialy  of  a  planet,  is  the  angle  at  the  sun  or  focus  of  the 
elliptical  orbit;  formed  by  the  line  of  apses  and  radius  vec- 


(     9     ) 

lor.  Excentric  anomaly,  is  the  angle  at  the  centre  of  the 
elliptical  orbit,  formed  by  the  line  of  apses  and  a  line  drawn 
to  the  point  in  which  an  ordinate  passing  through  the 
planet's  true  place  in  its  orbit,  meets  the  circumference 
of  a  circle,  described  on  the  line  of  apses  as  a  diameter. 
Mean  anomaly,  is  a  sector  of  the  elliptical  orbit  over 
which  the  radius  vector  has  passed,  from  the  aphelion  to 
the  place  of  the  planet  in  its  orbit ;  and  is  proportional  to 
the  time  of  description. 

Antarctic  circle.    See  Arctic  circle. 

Antipodes,  those  who  inhabit  parts  of  the  earth  diametrically 
opposite  to  each  other. 

Anticipation  of  the  equinoxes  or  seasons,  the  excess  of  the 
civil  Julian  year  of  365d.  6h.  above  the  solar  tropical 
year  of  365  days  5  hours  48  minutes  48  seconds.  This 
constitutes  the  difference  between  the  Julian  and  Grego- 
rian calendars,  or  old  and  new  styles. 

Aphelion,  is  that  point  of  a  planet's  orbit  which  is  at  the 
greatest  distance  from  the  sun. 

The  places  of  the  aphelia  of  the  several  planets  are  all 
different,  and  have  each  a  small  progressive  motion,  oc- 
casioned by  the  mutual  attractions  of  the  planets  on  each 
other. 

Apogee,\s  that  point  of  the  moon's  orbit  which  is  at  the  great- 
est distance  from  the  earth.  This  term  is  also  frequently 
applied  to  the  sun,  to  signify  that  point  in  which  he  is  at 
the  greatest  distance  from  the  earth. 

•Apses  or  apsides,  are  the  extremities  of  the  greater  axis  of 
the  planets'  elliptical  orbits  :  the  axis  itself  being  called 
the  line  oj"  the  apses. 

Arctic  circle,  is  a  small  circle  parallel  to  the  equator,  and  at 
the  same  distance  from  the  north  pole  that  the  tropics  are 
from  the  equator.  A  circle  similarly  situate  round  the 
south  pole,  is  called  the  antarctic  circle.  These  are  also 
frequently  termed  the  north-polar,  and  south-polar  circles^ 
respectively. 

Ascension  of  a  celestial  body,  is  an  arch  of  the  equator, 
reckoned  from  west  to  east,  and  intercepted  between  the 
equinoctial  point  Aries,  and  that  point  which  rises  with 
the  body.  This  is  distinguished  into  right,  and  oblique 
ascension,  according  to  the  angle  in  which  the  equator 
cuts  the  horizon. 

"Aspect,  is  a  term  applied  to  signify  the  situation  or  apparent 
distance,  in  longitude,  of  any  two  celestial  bodies  in  the 
zodiac,  from  one  another,  and  is  particularly  denominated, 
and  designated  by  appropriate  characters,  according  to 
this  distance — as  conjunction  &  ,  sextile  >K,  quartile  n? 
trine  A,  opposition  §  ,  and  some  others,  -which  s,ce. 

B 


Asteroids,  star-like  bodies,  a  term  of  recent  invention,  and 
applied  to  three  small  bodies  lately  discovered  in  the  so- 
lar system,  between  the  orbits  of  Mars  and  Jupiter.  Their 
orbits  are  considerably  more  excentric  than  that  of  any  of 
the  other  planets ;  though  their  elements  are  still  but  im- 
perfectly ascertained. — See  note  subjoined  to  the  Table 
of  the  solar  system,  page  73. 

Astronomy,  is  that  science  which  explains  and  demonstrates 
the  phenomena  of  the  heavens. 

Atmosphere,  usually  termed  the  air,  is  that  transparent  elas- 
tic fluid  which  surrounds  the  earth.  It  is  indispensably 
necessary  to  animal  and  vegetable  life,  combustion,  and 
many  other  functions  in  nature.  The  atmosphere  being  a 
perfectly  elastic,  compressible,  and  ponderous  fluid,  its 
density  must  decrease  upwards,  in  a  geometrical  ratio,  of 
the  heights  taken  in  arithmetical  ratio.  The  whole  weight 
of  any  column  of  the  atmosphere,  on  the  surface  of  the 
earth,  is  found,  by  experiment,  to  equal,  in  a  mean  state, 
that  of  a  column  of  mercury  of  an  equal  base  and  about 
30  inches  high ;  that  is,  about  15  pounds  avoir,  on  every 
superficial  inch.  The  planets,  if  not  the  sun  and  fixed 
stars,  are  all  probably  furnished  with  similar  atmospheres. 

Attraction,  is  that  power,  either  continually  exerted  by  the 
Deity,  according  to  a  fixed  law,  or  by  him  communicated 
to  matter  ;  by  which  all  bodies,  or  particles  of  bodies, 
whether  in  contact,  or  at  a  distance,  adhere,  or  tend  to- 
wards each  other.  Attraction,  according  to  the  manner 
or  circumstances  of  its  operation,  is  commonly  distin- 
guished into  that  of  gravity,  that  of  cohesion,  that  of  elec- 
tricity, &c. 

Axis  of  a  planet,  is  that  imaginary  line  passing  through  its 
centre,  round  which  it  performs  its  diurnal  rotation. 

Azimuth  of  a  celestial  body,  is  an  arch  of  the  horizon  inter- 
cepted between  the  meridian  of  the  place  and  the  azimuth- 
circle  passing  through  the  body.  The  true  azimuth  of  a 
body  may  readily  be  calculated  by  the  resolution  of  a  sphe- 
ric triangle ;  and  then  the  difference  between  this,  and 
that  observed  by  a  compass  furnished  with  a  magnetic 
needle,  will  be  the  -variation  of  the  compass. 

Azimuth-circles,  are  those  great  circles  of  the  sphere  which 
pass  through  the  zenith  and  nadir,  and  consequently  cross 
the  horizon  at  right  angles, 

Barometer,  is  an  instrument  for  measuring  the  weight  of  a 
superincumbent  column  of  the  atmosphere,  at  any  given 
time  and  place.  It  is  commonly  made  of  a  long  glass 
tube,  of  a  moderate  bore,  open  at  one  end  ;  which  being 
iilled  with  well-purified  mercury  is  inverted,  with  the 


11  ) 

o'pen  end  downwards,  into  a  bason,  of  the  same  fluid.  The 
mercury  in  the  tube  will  then  subside,  leaving  a  vacuum, 
in  the  upper  part  of  the  tube  ;  and  the  height  of  the  co- 
lumn of  mercury  in  the  tube,  thus  sustained  by  the  pres- 
sure of  the  atmosphere  on  the  surface  of  the  mercury  in 
the  bason,  will  be  a  just  measure  of  its  weight. 

It  is  found  by  experiment  that  the  height  of  the  column 
of  mercury  is  not  always  the  same  in  the  same  place,  but 
varies  generally  between  28  and  31  inches,  on  the  surface 
of  the  earth.  The  barometer  has  been  applied  with  suc- 
cess to  the  measuring  of  accessible  altitudes.  For  this 
purpose  let  the  height  of  the  mercury  in  a  barometer, 
both  at  the  bottom  and  top  of  the  eminence  or  depth  to 
be  measured,  be  observed  as  nearly  as  may  be  at  the  same 
time.  Also  observe  the  temperature  of  the  air  by  ther- 
mometers both  attached  to  the  barometers,  and  at  a  dis- 
tance from  them,  in  the  shade.  Then  let  the  column  of 
mercury  in  the  colder  barometer  be  increased  byits9600th 
part  for  every  degree  of  difference  in  the  two  attached  ther- 
mometers (Fahr.  scale).  Subtract  the  common  logarithm 
of  the  less  column  of  mercury  from  that  of  the  greater,  and 
the  difference  multiplied  by  10000  will  be  the  alt.  nearly, 
in  fathoms.  For  a  correction  apply,  by  addition  or  sub- 
traction, one  435th  part  of  the  above  alt.  for  every  degree 
of  the  mean  temperature  of  the  two  detached  thermo- 
meters above  or  below  3 1  degrees,  and  the  result  will  be 
the  true  alt. 

Bissextile,  a  year  consisting  of  366  days,  by  adding  a  day 
to  the  month  of  February  every  4th  year.  This  day  was 
by  Julius  Csesar  appointed  to  be  the  24th  of  March 
(called  by  the  Romans  the  6th  of  the  calends)  which  being 
reckoned  twice,  the  year  was  on  this  account  termed  bis- 
sextile. This  year  is,  on  another  account,  called  leap- 
year. 

Calendar,  is  a  table,  almanac,  or  distribution  of  time,  suited 
to  the  several  uses  of  society. 

Various  calendars  have  been  adopted  by  different  na- 
tions in  different  ages  of  the  world.— The  Roman  calen- 
dar, as  corrected  and  established  by  Julius  Caesar,  and 
thence  called  the  Julian  calendar,  made  the  year  to  con- 
sist of  365^  days ;  viz.  three  years  each  containing  365, and 
the  4th  366.  But  as  the  solar  year  actually  falls  short  ot 
the  Julian  by  about  11  minutes,  Pope  Gregory  XIII,  in 
1582,  reformed  this  calendar,  by  striking  out  the  surplus 
days  that  thefseasons  had  then  got  a-head  of  the  calendar ; 
(viz.  10  days)  and  ordering  that,  in  future,  3  days  should 
be  stricken  out  of  every  400  years  of  the  Julian  account, 
by  calling  every  centurial  year  not  devisible  by  4  (as  1700? 


(     12    ) 

1 800,  1900,  2100,  &c.)  a  common  year,  instead  of  a  leap- 
year.  The  year  is  divided  into  12  calendar  months,  viz. 
7  of  31  days,  4  of  30,  and  1  of  28  or  29. 

Central  forces,  are  those  by  the  influence  of  which  the  plan- 
ets and  comets  perform  revolutions  round  their  centres  of 
motion,  and  are  retained  in  their  orbits.  Those  forces 
are  of  two  kinds,  viz.  the  centrifugal,  and  the  centripetal. 

Centrifugal  or  projectile  force,  may  be  considered  as  a  sin- 
gle impulse,  given  by  the  Creator,  and  which,  agreeably 
to  the  laws  of  motion,  would  carry  the  body  with  a  uni- 
form velocity,  in  a  rectilineal  direction. 

Centripetal  force,  or  force  of  gravity,  may  be  considered  as 
a  continually-operating  influence,  urging  the  body  down 
towards  the  centre  of  motion  :  and  according  to  the  pro- 
portion between  these  two  forces  the  body  will  describe 
a  circular,  or  an  elliptical  orbit. 

Chronology,  is  that  science  which  treats  of  time,  compre- 
hending its  remarkable  aeras  or  epochs,  divisions,  subdi- 
visions, and  measures. 

Circle,  is  a  plane  figure  bounded  by  a  uniformly-curved  line 
called  the  circumference,  every  part  of  which  is  equally 
distant  from  a  certain  point  within  the  same,  called  the 
centre.  Diameter  is  a  right  line  passing  through  the  cen- 
tre, and  terminated  on  each  side  by  the  circumference. 
Radius,  or  semidiameter,  is  the  distance  from  the  centre 
to  the  circumference. 

Circles  of  the  sphere  are  of  two  kinds — great,  and  small. 
Great  circles,  are  those  which  divide  the  sphere  into  two 
equal  parts;  the  chief  of  which  are,  the  equator,  the  eclip- 
tic, meridians,  horizon,  azimuth-circles,  and  circles  of 
celestial  longitude.  Small  circles,  are  those  which  divide 
the  sphere  into  two  unequal  parts  ;  the  chief  of  which  are, 
parallels  of  altitude  and  of  depression,  parallels  of  terres- 
trial, and  parallels  of  celestial  latitude. 

Circles  of  celestial  longitude,  are  those  great  circles  of  the 
sphere  which  cross  the  ecliptic  at  right  angles. 

Circum-polar  stars,  are  those  which  appear  to  perform  daily 
circuits  round' the  pole,  without  rising  or  setting;  and  such 
are  all  those  whose  polar  distance  does  not  exceed  the  la- 
titude of  the  place. 

Colures,  are  those  two  meridians  which  pass  through  the 
equinoctial  and  solstitial  points  of  the  ecliptic,  and  are 
hence  distinguished  into  the  equinoctial  and  solstitial  co- 
lures. 

Comets,  are  certain  bodies  in  the  solar  system,  moving  in 
very  excentric  orbits,  in  various  planes  and  directions}, 
and  visible  but  for  a  short  time  when  near  their  perihe- 
lia ;  and  then  generally  appearing  with  a  lucid  tail  or  train 


(     13     ) 

of  light,  on  the  side  of  the  comet  opposite  to  the  suib 
Frequently,  however,  comets  are  seen  without  this  lucid 
train  ;  the  body  or  nucleus  being  surrounded  with  a  beard- 
ed or  hairy-like  atmosphere.  The  whole  list  of  comets 
that  have  been  hitherto  observed  amounts  to  upwards  of 
500  ;  of  which  about  170  have  been  observed  with  accu- 
racy, and  the  elements  of  their  orbits  computed. 

Conjunction,  is  that  aspect  in  which  two  celestial  bodies,  in 
the  zodiac,  have  the  same  longitude. 

Constellation-, — this  term  is  applied  to  any  assemblage  or 
number  of  neighbouring  stars  in  the  heavens,  which  as- 
tronomers have  classed  together  under  one  general  name. 
They  are  generally  designated  by  the  names  and  figures 
of  some  living  creatures,  and  thus  delineated  on  the  ce- 
lestial globe  or  atlas.  The  number  of  constellations,  ac- 
cording to  the  ancients,  was  48,  viz.  12  near  the  ecliptic, 
called  the  12  signs  of  the  zodiac,  21  on  the  north  side  of 
the  zodiac,  and  15  on  the  south  side.  Modern  astrono- 
mers, by  forming  new  constellations  out  of  such  stars  as. 
were  not  included  in  the  above,  have  increased  the  num- 
ber to  about  70 — The  several  stars  in  each  constellation 
are  distinguished  either  by  letters  of  the  alphabet,  or  by- 
numbers  :  and  some  few  by  proper  names ;  as,  Aldebaran, 
Castor,  Pollux,  Sec. 

Crepusculum  or  twilight-circle,  is  a  circle  of  depression,  1 8 
degrees  below  the  horizon  ;  for,  it  is  found  by  observation 
that  when  the  sun  crosses  this  circle,  before  rising,  or  af- 
ter setting,  twilight  begins  or  ends.  This  is  occasioned 
by  the  rays  of  light  from  the  sun  being  refracted  and  re- 
flected by  the  earth's  atmosphere. 

Culmination  .of  a  star,  is  the  point  of  its  greatest  elevation 
above  the  horizon,  or  where  it  crosses  the  meridian. 

Cusfis,  the  horns  of  the  moon,  or  any  other  planet,  when  less 
than  half  its  illuminated  part  is  visible. 

Cycle-,  is  any  certain  period  of  time  in  which  the  same  cir- 
cumstances, to  which  the  cycle  has  a  reference,  regularly 
return.  The  most  noted  chronological  cycles  are — 

1.  The  cycle  of  the  suti,  a  period  of  28  years,  after  which 
the  same  day  of  the  month  will  happen  on  the  same  day 
of  the  week,  as  in  the  same  year  of  a  former  cycle. 

2.  The  Metonic  or  lunar  cycle,  a  period  of  19  years, 
after  which  the  change,  full,  and  other  phases  of  the  moon, 
will  happen  on  the  same  days  of  the  month,  as  in  the 
same  year  of  a  former  cycle. 

3.  The  cycle  of  Indiction,  a  period  of  15  years,  instituted 
by  Constantine  A.  D.  312,  probably  as  a  stated  period  of 


(     14     ) 

levying  a  certain  tax,  and  afterwards  used  as  a  civil  epoch 
among  the  Romans. 

Note,  the  1st  year  of  the  Christian  aerawas  the  1st  af- 
ter leap-year,  the  9th  of  the  solar  cycle,  the  1st  of  the 
lunar  cycle,  and  the  312th  of  the  Christian  aera,  was  the 
1st  of  the  Roman  Indiction.  Hence  rules  may  be  easily 
deduced  for  computing  what  year  of  any  of  these  cycles, 
corresponds  to  any  given  year  of  the  Christian  sera. 
Day,  a  portion  of  time  measured  by  the  apparent  revolution 
of  the  sun,  moon,  or  stars,  round  the  earth.  The  day  is 
variously  distinguished  and  denominated,  according  to 
circumstances,  as  follows  : — 

1 .  An  artificial  day,  is  the  interval  of  time  between  sun- 
rising  and  sun-setting ;  and  thus  contradistinguished  from 
night  which  is  the  interval  between  sun-setting  and  sun- 
rising. 

2.  A  natural  day,  includes  both  the  artificial  day  and 
the  night. 

3.  An  afifiarent  solar  day,  is  the  time  in  which  the  sun 
appears  to  make  one  complete  revolution  round  the  earth. 
These  days,  owing  to  sundry  causes,  (see  equation  of  time} 
are  not  all  of  the  same  length,  but  continually  varying. 

4.  A  mean  solar  day,  is  an  exact  mean  of  all  the  appa- 
rent solar  days  in  the  year — Or  it  is  that  measured  by  a 
well-regulated  time-piece. 

5.  A  Lunar  day,  is  the  time  in  which  the  moon  appears 
to  make  one  complete  revolution  round  the  earth  ;  and 
exceeds  a  solar  day  about  f  of  an  hour. 

6.  A  sidereal  day,  is  the  time  in  which  any  fixed  star 
appears  to  make  a  complete  revolution?  and  is  3m.  5 5". 9 
less  than  a  raean  solar  day. 

The  day,  in  civil  reckoning,  begins  among  different  na- 
tions at  different  times. 

1.  Among  most  of  the  ancient  eastern  nations,  and 
some  of  the  modern,  it  begins  at  sun-rising. 

2.  Among  the  ancient  Athenians  and  Jews,  the  eastern 
parts  of  Europe,  and  the  modern  Italians  and  Chinese,  ft 
begins  at  sun-setting. 

3.  With  the  ancient  Arabians,  and  still  with  astrono- 
mers, it  begins  at  noon. 

4.  Among  the  ancient  Egyptians  and  Romans,   the 
Americans,  and  the  greater  part  of  Europeans,  it  begins 
at  midnight. 

Declination  of  a  celestial  body,  is  an  arch  of  the  meridian 
passing  through  the  body,  and  intercepted  between  it  and 
the  equator ;  and  is  north  or  south  according  as  the  body 
is  north  or  south  of  the  equator. 


(     15     ) 

Degree,  the  360th  part  of  the  circumference  of  any  circle.  Or 

the  90th  part  of  a  right  angle. 

Dial,  or  sun-dial,  is  a  delineation  of  the  meridians  of  the 
sphere,  on  a  plane,  in  such  a  manner  that  the  shadow  of 
a  gnomon  or  stile,  placed  with  its  edge  parallel  to  the 
Earth's  axis,  may  point  out  the  hour  of  the  day.  Dials 
are  particularly  denominated  from  the  planes  on  which 
they  are  drawn ;  as  horizontal,  equatorial,  &c. 
Digit,  the  1 2th  part  of  the  apparent  diameter  of  the  sun  or 
moon.  The  quantity  of  an  eclipse  is  generally  estimated 
by  the  digits  of  the  luminary's  diameter  eclipsed. 
Dip.,  the  depression  of  the  visible,  below  the  true  horizon, 
which  will  be  more  or  less  according  to  the  height  of  the 
eye.  The  dip  corresponding  to  any  given  height  of  the 
eye  may  be  very  readily,  and  very  accurately,  found  by 
the  following  theorem. 

d  =  tfh  —  £Q  yh  +  l";  in  which  h  =  height  of  eye 
in  feet,  and  d  —  the  dip  in  minutes  and  parts,  of  a  degree: 
thus  for  16  feet  the  dip,  per  rulerr=4'  — .2'  -f  1"=  3'  49". 
Direct  motion  of  a  planet,  in  its  orbit,  is  that  by  which  it 
appears  to  the  observer  to  move  according  to  the  order 
of  the  signs.  To  a  spectator  in  theu  sun,  the  planetary 
motions  would  always  appear  direct'.  To  a  spectator  in 
the  earth,  the  motions  of  Mercury  and  Venus  will  appeal- 
direct  when  they  are  in  the  superior  or  opposite  parts  of 
their  orbits  ;  and  the  motions  of  the  other  planets  will 
appear  direct  when  the  earth  is  in  the  opposite  part  of  its 
orbit  with  respect  to  them. 

Disc,  the  body  or  face  of  the  sun  or  moon  as  it  appears  to 
a  spectator  on  the  earth  ;  or  of  the  earth,  as  it  would  ap- 
pear to  a  spectator  in  the  moon, 

Dominical  letter.    In  the  Roman  calendar,  it  was  customary 
to  prefix  the  first  7  letters  of  the  alphabet  to  the  several 
days  of  the  week  throughout  the  year,  always  beginning 
the  year  with  the  letter  A.    The  letter,  then,  that  was 
prefixed  to  the  Sundays  (Dominici  dies)  throughout  the 
year,  was  called  the  Dominical  letter.  This  may  be  found 
for  any  year  of  the  Christian  sera,  by  the  following  rule. 
Divide  the  centuries  by  4,  subtract  twice  the  re- 
mainder from  6,  and  to  what  remains  add  the  odd  years 
and  their  4th  part,  rejecting  fractions  ;  divide  the  sum 
by  7,  and  then  the  remainder  taken  from  7  will  leave 
the  number  of  the  Dominical  letter  in  the  alphabet, 
Thus  for  the  year  1806  the  Dominical  letter  will  come 
out  5zrE. 


(     16     ) 

In  a  leap-year,  the  letter  thus  found  will  be  the  Domi- 
nical letter  till  the  28th  of  Feb.  and  the  preceding  one  will 
be  the  Dom.  let.  from  that  time  till  the  end  of  the  year. 

Earth,  the  third  planet  in  order  from  the  sun  ;  at  the  dis- 
tance of  about  95  millions  of  miles  ;  furnished  with  one 
moon. 

Eclipse.  When  any  secondary  planet  passes  through  the 
shadow  of  its  primary,  it  is  said  to  be  eclipsed ;  as  the 
moon  by  the  shadow  of  the  earth,  or  any  of  Jupiter's  sa- 
tellites by  his  shadow.  But  when  the  shadow  of  a  secon- 
dary planet  falls  on  its  primary,  then,  with  respect  to  that 
part  of  the  primary  on  which  the  shadow  falls,  the  sun  is 
said  to  be  eclipsed. 

Ecliptic  limit,  is  a  certain  distance  from  the  node  of  the 
secondary's  orbit,  beyond  which  no  eclipse  can  happen. 
This  limit  with  respect  to  a  solar  eclipse  is  about  17°. 
and  with  respect  to  a  lunar  eclipse,  about  12°. 

Ecliptic,  a  great  circle  of  the  sphere  in  the  plane  of  which 
the  earth  performs  its  annual  revolution  round  the  sun. 

Ellipse  or  ellipsis,  a  plane  curvilineal  figure,  which  may  be 
described  round  two  centres  thus. — Take  a  thread  of  any 
determinate  length,  tie  its  two  ends  "together,  and  throw 
the  loop  round  two  pins  stuck  into  a  plane  board — then 
moving  round  a  pencil,  or  the  like,  within  the  loop,  so  as 
to  keep  it  always  tight,  the  curve  described  will  be  an 
ellipsis. — .The  two  central  points  are  called  the  foci  of 
the  ellipsis  ;  a  right  line  passing  through  the  two  foci, 
and  terminated  by  the  curve  on  each  side,  is  called  the 
trans-verse  axis  or  diameter,  and  one  bisecting  this  at  right 
angles  is  called  the  conjugate. 

Elongation  of  a  planet,  (generally  applied  to  Mercury  and 
Venus)  their  angular  distance  from  the  sun  as  seen  from 
the  earth. 

Embolismic,  or 'intercalary,  a  term  applied  to  a  lunar  month 
occasionally  thrown  in  to  bring  up  the  lunar  to  the  solar 
years. — It  is  also  applied  to  the  29th  of  February,  thrown 
in  every  4th  year  to  make  the  civil  years  correspond  with 
the  solar. 

Emersion,  the  end  of  an  eclipse  or  of  an  occultation. 

Epact,  the  excess  of  solar  time,  above  lunar.  In  the  Gre- 
gorian calendar  it  is  the  moon's  age  at  the  beginning  of 
the  year,  which  may  be  found  by  the  following  rule,  till 
the  year  1900. 

Subtract  1  from  the  Golden  number,  multiply  the  re- 
mainder by  11,  and  the  product,  rejecting  the  30's,  will 
be  the  epact. 


(     17     ) 

See  jEra, 

Equation  of  time,  the  difference  between  apparent,  and  mean- 
solar  time.  This  arises  from  two  causes,  viz.  the  ellipti- 
cal figure  of  the  earth's  orbit  in  which  the  diurnal  arches 
will  of  consequence  be  unequal;  and  the  inclination  of  the 
the  ecliptic  to  the  equator,  whence  equal  arches  of  the 
former,  in  which  the  earth  moves,  will  not  correspond  to 
equal  arches  of  the  latter,  on  which  time  is  measured. 

Equator,  that  great  circle  which  cuts  the  axis  of  rotation  at 
right  angles. 

Equinoctial  points,  the  beginning  of  the  signs  Aries  and  Li- 
bra, those  two  points  of  the  ecliptic  in  which  it  crosses 
the  equator;  the  former  being  called  the  vernal,  and  the 
latter  the  autumnal,  equinoctial  point. 

Equinoxes,  the  times  when  the  sun  appears  to  enter  the 
equinoctial  points;  viz.  the  2 1st  of  March,  and  22d  of 
September. 

Excentricity,  or  eccentricity,  of  a  planet's  orbit,  is  equal  to 
half  the  distance  between  the  two  foci  of  the  elliptical 
orbit. 

Focus,  foci.     See  Ellipsis. 

Frigid  zones,  those  round  the  poles,  bounded  by  their  re* 
spective  polar  circles. 

Geocentric  jilace  of  a  planet,  is  its  place>  (generally  express- 
ed in  latitude  and  longitude,  or  right  ascension^  and  decli- 
nation) as  it  appears  from  the  earth* 

Globes  (artificial)  small  spheres  of  paste-board,  or  the  like, 
on  one  of  Which  (called  the  terrestrial  globe)  are  drawn 
the  principal  circles  of  the  sphere,  together  with  the  se- 
veral continents,  islands,  &c.  of  the  earth,  in  their  rela- 
tive situations  and  magnitudes.  On  the  other,  (called 
the  celestial  globe)  besides  the  circles  of  the  sphere,  are 
inserted  all  the  visible  fixed  stars,  distributed  into  their 
respective  constellations.  The  use  of  the  Globes,  explains 
the  manner  of  solving  geographical  and  astronomical  pro- 
blems, by  means  of  artificial  globes. 

Golden  number,  is  the  year  of  the  lunar  cycle,  increasing 
annually  by  unity  from  1  to  19. 

Gravity,  that  species  of  attraction  which  takes  place  be- 
tween bodies  at  a  distance  from  each  other,  and  by  which, 
if  not  otherwise  prevented,  they  would  mutually  approach 
each  other,  with  a  continually-accelerated  velocity.  Gra- 
vity is  directly  proportional  to  the  quantity  of  matter,  and 
inversely,  to  the  square  of  the  distance. 

Heliocentric  place  of  a  planet,  is  its  place  in  the  heavens,  as 
if  viewed  from  the  sun. 

*(   C    )* 


(     18     j 

Hcrschel,  or  Georgium  Sidus — the  7th  primary  planet  in  or- 
der from  the  sun,  at  the  distance  of  about  1800  millions 
of  miles.  It  is  furnished  with  6  satellites. 

Horizon,  that  great  circle  of  the  sphere  which,  extended  to 
the  heavens,  is  the  boundary  of  our  vision.  It  is  usually 
distinguished  into  sensible  or  visible,  and  rational  or 
true. 

TtJour,  the  24th  part  of  a  natural  day. 

Horary  angle  of  a  celestial  body,  an  angle  at  the  pole  of  the 
equator,  included  between  the  meridian  of  the  place  and 
that  passing  through  the  body. 

Immersion^  the  beginning  of  an  eclipse,  or  of  an  occultation. 

Inclination  of  the  axis  of  a  planet,  the  angle  which  it  makes 
with  the  axis  of  the  plane  of  its  orbit. 

Inclination  of  the  orbit  of  a  planet,  the  angle  in  which  it 
crosses  the  ecliptic. 

Jndiction,  (Roman).     See  Cycle. 

Jufiitcr,  the  fifth  primary  planet  from  the  sun,  at  the  dis- 
tance of  about  490  millions  of  miles.  It  is  the  largest  in 
the  system,  and  is  furnished  with  four  satellites. 

Latitude  of  a  filace  on  the  earth,  its  distance  from  the  equa- 
tor, measured  on  the  meridian  of  the  place. 

Latitude  of  a  celestial  body,  its  distance  from  the  ecliptic, 
measured  on  a  circle  of  celestial  longitude  passing  through 
the  body. 

Leap-yew,  one  of  366  days,  occurring  every  4th  year,  and 
so  called,  because  in  that  year  the  Dominical  letter  falls 
back  two  letters,  or  leaps  over  one.  See  Bissextile. 

Libration  of  the  moon,  a  small  apparent  libratory  motion, 
arising  chiefly  from  her  equable  rotation  round  her  axis, 
combined  with  her  unequal  motion  in  her  orbit. 

Longitude  of  a  place  on  the  earth,  an  arch  of  the  equator  in- 
tercepted between  the  prime  meridian,  and  that  passing 
through  the  place,  and  is  denominated  east  or  west,  ac- 
cording to  its  situation  with  respect  to  the  prime  meridian. 

Longitude  of  a  celestial  body,  an  arch  of  the  ecliptic,  reckon- 
ed according  to  the  order  of  the  signs,  from  the  equinoc- 
tial point  Aries  to  the  circle  of  celestial  longitude  passing 
through  the  body. 

Lunar  cycle.     See  Cycle. 

Mars,  the  fourth  primary  planet  from  the  sun,  at  the  dis- 
tance of  about  144  millions  of  miles. 

Meridians,  great  circles  crossing  the  equator  at  right  angles. 

Meridian  of  the  place,  that  passing  through  the  north  am! 
south  points  of  the  horizon. 


(     19     ) 

Midheaven,  that  point  of  the  ecliptic,  or  of  the  equator, 

which  is  in  the  meridian. 

Minute,  the  60th  part  of  an  hour,  or  of  a  degree. 
Month,  the  12th  part  of  a  year.    It  is  variously  distinguish- 
ed according  to  circumstances,  viz. 

Lunar  illuminative  month,  the  time  between  the  first  ap- 
pearance of  one  new  moon,  and  of  the  next.  The  an- 
cient Jews,  with  the  'Turks  and  Arabs,  reckon  by  this 
month. 

Lunar  periodical  month,  the  time  in  which  the  moon  ap- 
pears to  make  a  revolution  through  the  zodiac  =  27  d, 
7  h.  43  m.  8  s. 

Lunar  si/nodical  month,  or  lunation,  the  time  between  one 
new  moon,  or  conjunction  of  the  sun  and-moon,  and  the 
next:  at  a  mean  ==  29d.  12h.  44m.  3s.  lit. 
Solar  month,  the  12th  part  of  a  solar  tropical  year  =  30d. 

lOh.  29m.  5s. 

Calendar  months,  those  made  use  of  in  the  common  reck- 
oning of  time,  as  in  Almanacs  or  Calendars. 
The  judicial  month,  consists  of  4  weeks  or  28  days. 
Moon,  the  satellite  or  secondary  of  the  Earth,  at  the  dis- 
tance of  about  240  thousand  miles. 
J\1idir,  the  lower  pole  of  the  horizon. 

JVodes  of  a  planet's  orbit,  {those  two  points  in  which  it  cros- 
ses the  ecliptic.  That  in  which  the  planet  passes  from 
the  south  side  of  the  ecliptic  to  the  north,  is  called  its  as- 
cending node  or  dragon's  head  SI ,  and  the  opposite  point, 
its  descending  node,  or  dragon's  tail  ^ .  The  nodes  of  all 
the  planets'  orbits  have  a  slow  retrograde  motion,  occasion- 
ed by  their  moving  in  different  planes,  and  their  mutual 
attraction  on  each  other. 
.Vonagesimal,  that  point  in  the  ecliptic  which  is  90°  from  the 

horizon. 

Nutation  of  a  star,  a  small  apparent  motion,  occasioned  by 
the  variable  attraction  of  the  sun  and  moon  on  the  sphe- 
roidal figure  of  the  earth;  by  which  the  axis  is  made  to 
revolve  with  a  conical  motion,  the  extremities  or  poles 
describing  in  i8y.  7m.  the  lunar  period,  or  revolution  of 
the  moon's  nodes,  a  small  ellipse  whose  transverse  diame- 
ter =  19".l  and  conjugate  =  14//.2.  The  correction  of 
the  right  ascension  and  declination  of  a  star  arising  from 
this  cause  may  be  readily  found  by  the  following  theo- 
rems: in  which  A  —  the  right  ascension  of  the  star  (per 
table),  I)  =  its  declination,  and  N  =  the  longitude  of  the 
moon's  ascending  node. 

Th.  1.  —  8".3  cos.  (N  —  A)  tan.  D  —  l".25  cos.  (N  -f 
A)  tan.  D  —  16". 2 5  sin.  N.  =  the  nutation  in  Rt.  as.  in 
seconds  of  time. 


Th.  2.  4-  9".55  cos.  N.  sin.  A  +*7".05  cos.  A  sin.  N  = 
the  nutation  in  cleclin.  in  seconds  of  a  degree.  The  up* 
per  signs  are  to  be  used  when  the  star  has  north  dec. 
and  the  under  signs  when  it  has  south  dec.  See  Aberra- 
tion. 

Oblique  ascension  of  a  celestial  body,  that  point  of  the  equa/< 
tor  which  rises  at  the  same  time  with  the  body  in  an  ob- 
lique sphere. 

Obliquity  of  the  ecliptic,  the  angle  in  which  the  ecliptic  cros- 
ses the  equator. 

Occultatio?i  of  a  star,  the  moon's  passing  between  the  star 
and  the  observer,  and  thereby,  for  a  time,  hiding  it  from 
his  sight. 

Olympiads.  Games  celebrated  by  the  Greeks  every  4  years. 
See  jEra. 

Opposition,  that  aspect  in  which  the  difference  of  longitude 
of  the  two  bodies  is  180°. 

Orbit  of  a  planet,  the  path  in  which  it  revolves  round  its 
centre  of  motion.  The  orbits  of  all  the  planets,  whether 
primary  or  secondary,  are  elliptical,  though  of  but  small 
excentricity;  and  all  (with  the  exception  of  lierschel's 
satellites)  nearly  in  the  plane  of  the  ecliptic,  or  earth's 
orbit. 

Parallax  of  a  celestial  body,  is  equal  to  the  angle  at  the  body, 
subtended  by  a  semidiameter  of  the  earth  terminating  in 
the  place  of  the  observer.  Hence  the  horizontal  parallax 
of  a  body  will  be  the  greatest,  and  in  the  zenith  it  will 
entirely  vanish.  The  fixed  stars,  from  their  immense  dis- 
tance, have  no  sensible  parallax. 

Parallax  of  the  earth's  annual  orbit,  at  a  planet,  is  the  angle 
at  that  planet  subtended  by  the  distance  between  the  earth 
and  sun. 

Penumbra,  a  faint  or  imperfect  shade,  observed  in  eclipses, 
and  occasioned  by  a  partial  interception  of  the  sun's  light. 

Perigee,  that  point  of  the  moon's  orbit  which  is  nearest  to 
the  earth.  The  term  is  sometimes  applied  to  signify 
that  point  in  which  the  sun  is  nearest  to  the  earth. 

Perihelion,  that  point  of  a  planet's  orbit  which  is  nearest  to 
the  sun. 

Periodical  time  of  a  planet,  that  in  which  it  performs  a  com- 
plete revolution  round  its  centre  of  motion. 

Perioeci,  such  as  live  in  opposite  points  of  the  same  parallel 
of  latitude. 

Periscii,  those  whose  shadows  turn  quite  round  during  the 
day,  the  sun  not  setting — and  such,  at  certain  times  of 
the  year,  are  the  inhabitants  of  the  frigid  zones. 


(     21     ) 

Phases  of  a  planet,  the  various  appearances  of  the  visible 
illuminated  part,  as  horned,  half  illuminated,  gibbous, 
full. 

Planets,  bodies  in  the  solar  system,  which  revolve  in  orbits 
nearly  circular,  and  all  nearly  in  the  same  plane.  They 
are  distinguished  into  primary,  and  secondary. 

The  primary  jilanets,  revolve  round  the  sun  as  their 
centre,  and  the  secondaries,  round  their  respective  prima- 
ries as  their  centres. 

The  table  at  the  end  of  this  Glossary  contains  a  correct 
synopsis  of  the  distances,  magnitudes,  periods,  and  all 
the  other  important  elements  of  the  several  planets,  both 
primary  and  secondary,  in  the  solar  system,  according  to 
the  latest  observations.  The  sun's  horizontal  parallax, 
as  determined  from  the  transit  of  Venus  in  1769,  being 
8"|. 

Poles  of  any  great  circle  of  the  sphere,  two  opposite  points 
in  the  surface  of  the  sphere,  each  90  degrees  distant  from 
the  circumference  of  the  given  circle. 

Precession,  recession,  or  retrocession  of  the  equinoxes,  a 
slow  motion  of  50"^  per  year,  by  which  the  equinoctial 
points  of  the  ecliptic  are  carried  backwards  from  east  to 
"west,  and  consequently  the  epliptical  stars  carried  forwards 
from  west  to  east. 

This  motion  is  occasioned  by  the  attraction  of  the  sun 
and  moon,  on  the  matter  of  the  earth  accumulated  at  the 
equator  by  its  diurnal  rotation. 

Primary  planets-,  those  bodies  in  the  solar  system  which  re- 
volve round  the  sun  as  their  centre  of  motion,  in  orbits 
nearly  circular. 

Prime  -vertical,  that  azimuth-circle  which  passes  through 
the  east  and  west  points  of  the  horizon. 

Quadrature,  or  quartile,  that  aspect  in  which  the  bodies  have 
90°.  difference  of  longitude. 

Radius  -vector  of  a  planet,  the  distance  from  the  planet,  in 
any  give'n  part  of  its  orbits,  to  the  centre  of  motion. 

Refraction  of  a  celestial  body,  the  angle  in  which  the  rays 
of  light  coming  from  the  body,  are  bent  downwards  from 
their  right  course  in  falling  obliquely  upon,  and  passing; 
through,  the  earth's  atmosphere.  This  is  greatest  in  the 
horizon,  and  entirely  vanishes  in  the  zenith. 

Retrograde  motion  of  a  planet,  that  by  which  it  appears  to 
the  observer  to  move  contrary  to  the  order  of  the  signs. 
To  a  spectator  on  the  earth,  Mercury  and  Venus  will  ap- 
pear retrograde  when  they  are  in  the  inferior  or  nearer 
part  of  their  orbits,  and  all  the  other  planets  will  appear 


retrograde  when  the  earth  is  in  the  nearer  part  of  its  or- 
bit with  respect  to  them. 

Satellites,  or  secondary  planets,  or  moons,  those  smaller 
bodies  in  the  solar  system  which  regard  the  primaries  as 
their  centres  of  motion. 

'Saturn,  a  primary  planet,  the  6th  in  order  from  the  sun,  at 
the  distance  of  about  900  millions  of  miles.  It  is  furnish- 
ed with  a  stupendous  double  ring  and  7  satellites. 

Second,  the  60th  part  of  a  minute,  whether  of  time  or  of  a 
degree. 

Sex  tile,  that  aspect  where  the  difference  of  longitude  of  th'e 
two  bodies  =  60°. 

Sign  of  the  ecliptic,  an  arch  of  30°.  or  the  12th  part  of  the 
whole  circle. 

Signs  of  the  zodiac,  twelve  constellations,  distributed  through 
the  zodiac,  and  nearly  at  equal  distances.  The  vernal  equi- 
noctial point  was  formerly  in  the  constellation  Aries,  but 
owing  to  the  precession  of  the  equinoxes  it  is  now  in  the 
constellation  Pisces;  yet  the  artificial  signs  continue  to  be 
called  by  their  former  names.  The  equinoctial  points  be- 
ing still  denominated  Aries  and  Libra,  and  the  solstitial 
points,  Cancer  and  Capricorn. 

Solar  system,  comprehends  the  sun,  the  centre  of  the  sys- 
tem, the  primary  planets,  the  secondary  planets,  and  the. 
comets. 

Solar  cycle. —See  Cycle. 

Solstices,  the  times  when  the  sun  enters  the  two  solstitial 
points  of  the  ecliptic,  viz.  the  21st  of  June,  the  time  of 
the  northern  solstice,  and  the'  22d  of  December,  that  of 
the  southern  solstice.  These  with  relation  to  the  north- 
ern hemisphere,  are  frequently  denominated  the  summer, 
and  winter,  solstices,  respectively. 

Solstitial  points  of  the  ecliptic,  those  opposite  points  in  which 
the  sun  has  the  greatest  declination,  viz.  the  beginning  of 
the  sign  Cancer  in  the  northern  hemisphere,  and  the  be- 
ginning of  the  sign  Capricorn,  in  the  southern. 

Sphere,  in  a  geometrical  sense,  is  a  solid  contained  under  a 
uniformly-curved  surface,  every  point  of  which  is  equally 
distant  from  a  certain  point  within  the  same,  called  the 
centre.  This  term  is  applied  to  the  several  celestial  bo- 
dies, as  they  are  probably  all  nearly  of  this  figure.  It  is 
also  applied  to  the  apparent  concave  surface  of  the  hea- 
vens, and  is  then  called  the  celestial  sphere. 

The  sphere,  in  geography  and  astronomy,  is  frequently 
distinguished  by  the   epithets  right,  oblique,  or  parallel? 
according  to  the  position  of  the  equator  and  horizon: 
bright  sphere,  is  that  in  which  the  equator  cuts  tUe  he- 


(     23     } 

rizon  at  right  angles,  and  such  is  the  case  to  an  inhabitant 
at  the  equator.  In  this  sphere  the  lengths  of  the  days 
and  nights  are  always  equal. 

dn  oblique  sphere,  is  that  in  which  the  equator  cuts  the 
horizon  at  oblique  angles;  and  such  is  the  case  to  any 
inhabitant  north  or  south  of  the  equator.  In  this  sphere 
the  lengths  of  the  days  and  nights  are  always  varying — 
the  variation  being  greater,  the  greater  the  latitude. 

A  parallel  sphere,  is  that  in  which  the  equator  is  parallel, 
or  rather  coincident,  with  the  horizon;  and  such  is  the 
case  to  an  inhabitant  at  either  pole.  In  this  sphere,  the 
sun  Will  be  six  months  successively  visible,  and  six  in- 
visible. . 

Spheroid,  a  solid  which  may  be  conceived  as  generated  by 
the  rotation  of  an  ellipsis  round  its  tranverse  or  conju- 
gate diameter.  In  the  former  case,  the  spheroid  is  said 
to  be  prolate,  and  in  the  latter,  oblate.  The  figure  of  the 
earth,  and  perhaps  that  of  most  of  the  other  planets,  is  near- 
ly that  of  an  oblate  spheroid.  This  arises  from  their  rotato- 
ry motion  round  their  axes,  by  which,  the  attraction  at  the 
surface  is  continually  diminished  from  the  poles  to  the 
equator,  by  the  Continued  increase  of  the  centrifugal  force; 
and  thus,  the  equatorial  diameter  becomes  greater  than 
the  polar.  It  follows  from  this  figure,  that  the  length  of 
the  degrees  of  latitude  gradually  increase  from  the  equa- 
tor to  the  poles.  To  this  figure  of  the  earth  we  are  to 
ascribe  many  of  the  apparent  irregularities  in  the  motions 
of  the  celestial  bodies:  as,  the  precession  of  the  equinoxes, 
the  nutation  of  th6  stars,  Sec. 

'  Stars,  or  fixed  stars,  luminous  bodies,  at  an  immense  dis- 
tance, appearing  in  all  parts  of  the  heavens.  They  all 
probably  resemble  the  sun  in  matter  and  in  magnitude, 
and  are  each  the  centre  of  a  system,  similar  to  the  solar 
system.  They  are  said  to  be  fixed  because  they  con- 
stantly preserve,  very  nearly,  the  same  relative  position 
to  each  other.  Besides  the  small  apparent  motion  of  the, 
stars  arising  from  aberration,  and  nutation,  and  the  pre- 
cession of  the  equinoxes;  in  some  of  them  there  has  been 
discovered  a  very  slow  (indeed)  proper  motion.  Whence 
it  is  conjectured  that  not  only  the  bodies  belonging  to  the 
innumerable  systems  of  stars  are  in  motion  round  theu' 
respective  centres,  but  that  all  the  systems  of  bodies  in 
the  universe  are  themselves  in  motion  round  some  com- 
mon centre — and  that  thus  they  are  prevented  from  ap- 
preaching  each  other,  which,  from  their  mutual  attrac- 
tions, they  must  otherwise  do. 


(     24     ) 

Stationary.  This  term  is  applied  to  a  planet,  when,  for  some 
time,  it  appears  to  a  spectator  to  occupy  the  same  place 
in  the  zodiac.  To  a  spectator  in  the  sun,  the  planets' 
motions  would  always  appear  direct;  and  that  they  ever 
appear  otherwise  to  a  spectator  on  the  earth,  is  owing  to 
its  own  motion,  and  being  placed  out  of  the  centre  of  the 
system.  To  such  a  spectator,  Mercury  and  Venus  will 
appear  stationary  when  at  their  greatest  elongation;  and 
all  the  other  planets  will  appear  stationary  when  the  earth 
is  at  its  greatest  elongation  with  respect  to  them. 

Style,  the  particular  manner  of  counting  time.  It  is  dis- 
tinguished into  old  and  new. 

Old  style,  is  that  which  follows  the  Julian  calendar. 
New  style,  is  that  which  follows  the  Gregorian  calendar. 
See  Calendar.     In  the  year  1800  the  latter  was  12  days 
ahead  of  the  former,  and  in  every  centurial  year  not  divi- 
sible by  4,  the  difference  will  be  increased  1  day. 

Systems  of  the  Universe.  Of  these  there  are  3  noted  ones 
in  the  history  of  astronomy,  viz.  the  Ptolemean  system, 
advocated  by  many  of  the  ancient  philosophers.  Accord- 
ing to  this,  the  earth  occupies  the  centre  of  the  universe* 
and  is  at  rest;  while  all  the  celestial  bodies  revolve  round 
it  from  east  to  west,  every  24  hours.  The  Tychonean  nys- 
tcm,  invented  by  Tycho  Brahe,  a  noted  Danish  Astrono- 
nomer,  bom  A.  D.  1546.  According  to  this  system,  the 
earth,  as  in  the  Ptolemean  system,  is  placed  in  the  centre 
of  the  universe,  the  moon  revolving  round  the  earth  as 
her  proper  centre,  while  the  sun,  with  all  the  other  pla- 
nets moving  round  him  as  satellites,  revolve  also  round 
the  earth. 

Cofiernican  system,  maintained  by  many  of  the  ancients, 
particularly  by  Pythagoras,  revived  by  Copernicus  a  na- 
tive of  Thorn  in  Prussia  (born  1473),  and  demonstrated 
by  Sir  Isaac  Newton.  According  to  this  it  is  demon- 
strated that  the  sun  is  the  centre  of  the  planetary  sys- 
tem; the  primary  planets  revolving  round  him  in  their 
annual  orbits,  and  the  secondaries  round  their  respective 
primaries.  That  the  orbits  both  of  the  primary  and  se- 
condary planets  are  all  nearly  circular,  though  in  fact  ellip- 
tical; the  sun,  or  primary,  being  placed  in  one  of  the 
foci  of  the  respective  orbits.  That  they  all  lie  nearly  in 
the  same  plane.  That  all  the  planets  revolve  nearly  in 
the  same  direction,  the  square  of  their  periodical  times 
being  directly  proportional  to  the  cubes  of  their  mean 
distances  from  the  centre  of  motion.  That  the  earth, 
and  perhaps  most,  if  not  all  the  other  primary  planets. 


(     25     ) 

perform  a  diurnal  rotation  round  their  axes  ;  and  that  the 
moon,  or  satellite  of  the  earth,  as  well  as  perhaps  all 
the  other  satellites,  constantly  present  the  same  face  to- 
wards their  primaries.  That  the  inclination  of  the  axis 
of  rotation  to  the  plane  of  the  ctbit  is  different  in  differ- 
ent planets  ;  and  that  thus  they  experience  a  differenc6 
in  their  diversity  of  seasons. 

Syzigy.  This  general  term  is  applied  both  to  signify  the  con. 
junction  and  opposition  of  a  planet  with  the  Sun. — It  is 
however  chiefly  used  in  relation  to  the  moon. 
Tides,  a  periodical  alternate  motion  or  flux  and  reflux  of 
the  waters  of  the  sea. 

These  are  caused  chiefly  by  the  attraction  of  the  moon, 
though  in  part  by  that  of  the  Sun  also  ;  and  accordingly 
there  are  two  tides  of  flood  (and  consequently  two  of 
ebb)  in  the  course  of  every  lunar  day.  The  apex  of  one 
of  the  tides  of  high  water  is  immediately  under,  or  ra- 
ther about  45°  eastward  of,  the  moon;  and  the  other,  dia- 
metrically opposite.  These  are  produced  by  the  unequal 
attractions  of  the  moon  on  the  part  of  the  eatth  nearest 
to  her,  on  the  centre  of  the  eartii,  and  on  the  part  farthest 
from  her  (attraction  decreasing  inversely  with  the  square 
of  the  distance.)  One  tide  therefore  is  produced  by  a  re- 
dundancy of  attraction,  drawing  the  waters  up  towards 
the  moon,  and  the  opposite  tide,  .by  a  deficiency  of  attrac- 
tion, leaving,  as  it  were,  the  waters  behind.  When  the 
sun  and  moon  are  in  conjunction  or  opposition,  the  tides, 
being  then  produced  by  their  joint  influence,  are  higher 
than  usual,  and  hence  called  spring -tides  ;  but  when  these 
bodies  are  in  quadrature,  the  tides,  being  produced  by  the 
difference  of  their  influence,  are  lower  than  usual,  and 
hence  called  neap-tides  L 

Time  is  measured  by  the  apparent  motion  of  the  celestial 
bodies ;  and  is  variously  distinguished  :  thus — 

Apparent  solar  time,  is  that  measured  by  the  apparent 
motion  of  the  sun ;  and  hence  the  apparent  solar  time 
from  noon,  is  equal  to  the  sun's  horary  angle  reduced  to 
time,  at  the  rate  of  15°  to  the  hour. 

Mean  solar  time,  is  that  shewn  by  a  true  time-piece, 
going  with  an  equable  motion  throughout  the  year. 

Sidereal  time,  is  that  measured  by  the  apparent  equa- 
ble motion  of  the  stars. 

Lunar  time,  that  measured  by  the  apparent  motion  of 
the  moon.  See  Day. 

Transit  of  an  inferior  planet  (Mercury  or  Venus)  over 
the  sun's  disc,  is  when  the  planet,  at  the  time  of  an  in- 
ferior conjunction,  passes  between  the  sun  and  the  ob- 

C 


(     26     J. 

server.  This  will  only  happen  when  the  planet,  at  the  time? 

of  this  conjunction,  is  in  or  near  its  node. 

Trine,  an  aspect  where  the  bodies  are  at  the  distance  of 

i.  of  the  ecliptic  or  120°a 

Twilight.     See  Crepusculum. 

Venus,  the  second  primary  planet  from  the  sun,  at  the 
distance  of  about  68  millions  of  miles. 

Fear,  a  period  of  time  generally  considered  as  compre- 
hending a  complete  revolution  of  the  seasons.  The  year 
is  variously  distinguished,  viz. 

1 .  Tropical  Solar  year,  the  time  in  which  the  sun  appears 
to  perform  a  complete  revolution  through  all  the  signs  of 
the  zodiac  =  365d.   5h.  48m.  48s. 

2.  Sidereal  year,  the  time  in  which  the  sun  appears  to 
revolve  from  any  fixed  star  to  the  same  again  =  365d.  6h. 
9m.   17s.     The  difference  between  the  tropical  and  sidereal 
year  (20m.  29s.)  is  the  time  of  the  sun's  apparent  motion 
through  50"1,  the  arch  of  annual  precession. 

3.  Lunar  astronomical  year,  consists  of   12  lunar  synodi- 
cal  months  =  354d.  8h.  48m.  38s.  and  therefore  10d.21h.0m. 
1.0s.    less  than  the    solar  year — a  difference  which  is  the 
foundation  of  the  epacU 

4.  The  common  lunar  civil  year,  consists  of  12  lunar  civil 
months,  =  324  days 

5.  The  embolismic  or  intercalary  lunar  year,,  consists  of 
13  lunar  civil  months  =  384  days. 

6.  The  common  civil  year,  contains  365  days,  divided  into 
12  calendar  months. 

7.  Bissextile  or  leap-year,  containing  366  days.     See  cal- 
endar. 

Zenith,  the  upper  pole  of  the  horizon. 

Zenith-distance  of  a  celestial  bod),  its  distance  from  the  ze- 
nith, measured  on  the  azimuth-circle  passing  through  the 
body,  and  is  equal  to  the  complement  of  the  altitude  to  90°, 
Zodiac,  a  zone  or  broad  circle  in  the  heavens  including  alt 
the  planets,  and  extending  about  10°.  on  each  side  of  the 
ecliptic. 

Zodiacal  light,  a  pyramidal  lucid  appearance,  sometimes  ob- 
served in  the  zodi.ic,  resembling  the  galaxy,  or  milky 
way.  It  is  most  plainly  observable  after  the  evening  twi- 
light about  the  latter  end  of  February ;  and  before  the 
rooming  twilight  about  the  beginning  of  October.  For  at 
these  times  it  appears  near.y  perpendicular  to  the  horizon. 
This  appearance  is  generally  supposed  to  be  occasioned 
by  the  sun's  atmosphere. 


(     27     ) 

in  astronomical  geography?  is  applied  to  a  division  ot 
the  earth's  surface  by  certain  parallels  of  latitude. 
The  Zones  are  5  in  number,  viz. 

1.  The  torrid  zone,   lying  between  the  two  tropics.     It 
comprehends  the  West  India  Islands,   the  greater  parts 
of  South  America  and  of  Africa,  the  southern  parts  of 
Asia,  and  the  East  India  Islands. 

2.  The  north  frigid  zone,  lying   round  the  north  pole, 
and  bounded  by  the  north  polar  circle.     It  comprehends 
part  of  Greenland,   of  the  northern  regions    of  North 
America,  and  a  little  of  the  northern  parts  of  Europe 
and  Asia. 

3.  The  south  frigid  zone,   lying  round  the  south   pole, 
and  bounded  by  the  south  polar  circle.     It  contains  no 
dry  land,  so  far  as  yet  discovered. 

4.  The  north  temfierate  zone,  lying  between  the  torrid 
and  north  frigid.    It  comprehends  almost  the  whole  of 
North  America,   Europe,  and  Asia,  with  the  northern 
part  of  Africa. 

5.  The  south  temfierate  zone,  lying  between  the  torrid 
and  south  frigid.     It  comprehends  the  southern  part  of 
South  America,  of  Africa,  and  of  the  great  island  of  New- 
Holland. 

In  the  torrid  zone,  the  sun  is  vertical  twice  a  year  to 
every  part  of  it,  and  there  is  very  little  diversity  in  the 
length  of  the  clay  throughout  the  year,  the  longest  clay 
varying  only  from  12  to  about  13J  hours.  In  the  tempe- 
rate zones  the  sun  is  never  vertical,  and  the  length  of  the 
longest  day  varies  from  about  13|  to  24  hours.  In  the 
frigid  zones,  the  length  of  the  longest  day  (or  time  be- 
tween the  sun's  rising  and  setting)  varies  from  24  hours 
to  6  months. 


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CONTENTS. 


PAGE. 

Explanation  of  the  principal  Terms  relating  to  As- 

f  tronomy,    Chronology,    and    the    astronomical 

Parts  of  Geography,  with  occasional  Illustra- 

trations  and  Remarks,  .  •  .         .         5 

*>  Table   of   the   Motions  and    Distances   of   the 

Planets,  28 

Table  of  the  Satellites 29 

CHAP.  I.     Of  Astronomy  in  general, 

II.     A  brief  Description  of  the  SOLAR  SYSTEM,  40 

III.  The  COPERNICAN  SYSTEM  demonstrated  to  be 

true, 77 

IV.  The  Phenomena  of  the  Heavens  as  seen  from  dif- 

ferent Parts  of  the  Earth,          ....      89 

V.  The  Phenomena  of  the  Heavens  as  seen  from  differ- 

ent Parts  of  the  Solar  Sytem,  .         .        .       97 

VI.     The  Ptolemean  System  refuted.   The  Motions  and 

Phases  of  Mercury  and  Venus  explained,         .     102 
VII.    The  physical  Causes  of  the  Motions  of  the  Planets. 
The  Excentricities  of  their  Orbits.    The  Times 
i   in  which  the  Action  of  Gravity  would   bring 
them  to  the  Sun.  ARCHIMEDES'  ideal  Problem 
for  moving  the  Earth.    The  World  not  eternal,  109 
VIII.     Of  Light.     Its  proportional  Quantities  on  the  dif- 
ferent Planets.    Its  Refractions  in  Water  and 
Air.  The  Atmosphere  ;  its  Weight  and  Proper- 
ties.   The  horizontal  Moon,  .        .         .118 
IX.    The  Method  of  finding  the  Distances  of  the  Sun, 

Moon,  and  Planets, 134 

X.  The  Circles  of  the  Globe  described.  The  different 
Lengths  of  Days  and  Nights,  and  the  Vicissi- 
tudes of  Seasons,  explained.  The  Explanation  of 
the  Phenomena  of  Saturn's  Ring,  concluded,  142 
XI.  The  Method  of  finding  the  Longitude  by  the 
Eclipses  of  Jupiter's  Satellites  The  amazing 
Velocity  of  Light  demonstrated  by  these  Eclip- 
ses,   154 

XII.     Of  Solar  and  Sidereal  Time,         .         .         .        .162 

XIII.  Of  the  Equation  of  Time,  .         .         .        .167 

XIV.  Of  the  Precession  of  the  Equinoxes,  .         .     183 
XV.     The  Moon's  Surface   mountainous :    Her  Phases 

described :  Her  Path,  and  the  Paths  of  Jupi- 
ter's Moons  delineated  :  The  Proportions  of  the 
Diameters  of  their  Orbits,  and  those  of  Saturn's 
Moons  to  each  other,  and  to  the  Diameter  of 
the  Sun,  219 

XVI.  The  Phenomena  of  the  Harvest-Moon  explained  by 

a  common  Globe:  The  Years  in  which  the 
Harvest-Moons  are  least  and  most  beneficial, 
from  1751  to  1861  The  long  Duration  of  Moon- 
light at  the  Poles  in  Winter,  .  ,  .  235 

XVII.  Of  the  Ebbing  and  Flowing  of  the  Sea,  .    251 


CONTENTS. 

PAGE. 

CHAP.  XVIII.  Of  Eclipses:  Their  Number  and  Periods.  A  large 

Catalogue  of  Ancient  and  Modern  Eclipses,        263 
XIZ.     Shewing  the  Principles  on  which  the  following 
Astronomical  Tables  are  constructed,  and  the 
Method  of  calculating  the  Times  of  New  and 
Full  Moons  and  Eclipses,  by  them,  .        .     320 

XX.     Of  the  fixed  Stars,  370 

XXI.  Of  the  Division  of  Time.  A  perpetual  Table  of 
New  Moons  .  The  Times  of  the  Birth  and  Death 
of  CHRIST.  A  Table  of  remarkable  ./Eras  or 

Events,  391 

XXII.     A   Description  of   the  astronomical   Machinery, 
serving  to  explain  and  illustrate  the  foregoing 

Part  of  this  Treatise, 432 

XXIII.     The  Method  of  finding  the  Distances  of  the  Planets 

from  the  Sun,  465 

ART.  I.     Concerning  Parallaxes,  and  their  Use  in  general,    467 
AIIT.  II.    Shewing  how  to  find  the  horizontal  Parallax  of 
Venus   by  Observation,  and  from   thence,   by 
Analogy,  the  Parallax  and  Distance  of  the  Sun, 
and  of  all  the  Planets  from  him,  .         .    472 

ART.  III.  Containing  Doctor  HALLEY'S  Dissertation  on 
the  Method  of  finding  the  Sun's  Parallax  and 
Distance  from  the  Earth,  by  the  Transit  of 
Venus  over  the  Sun's  Disc,  June  the  6th,  1761. 
Translated  from  the  Latin  in  Matte's  Abridg- 
ment of  the  Philosophical  Transactions,  Vol.  I. 
page  243 ;  with  additional  Notes,  .  .  482 

ART.  IV.     Shewing  that  the  whole  Method  proposed  by  the 

Doctor  cannot  be  put  in  Practice,  and  why,         498 
ART.  V.     Shewing  how  to  project  the  Transit  of  Venus  on 
the  Sun's  Disc,  as  seen  from  different  Places  of 
the  Earth  ;  so  as  to  find  what  its  visible  Dura- 
tion must  be  at  any  given  Place,  according  to 
any  assumed  Parallax  of  the  Sun  ;  and  from  the 
observed  Intervals  between  the  Times  of  Ve- 
nus's  Egress  from  the  Sun  at  particular  Places, 
to  find  the  Sun's  true  horizontal  Parallax,        .     500 
ART.  VI.     Concerning  the  Map  of  the  Transit,  .         .     520 

ART.  VII.  Containing  an  Account  of  Mr.  HORROX'S  Observa- 
tion of  the  Transit  of  Venus  over  the  Sun,  in 
the  Year  1639  ;  as  it  is  published  in  the  Annual 
Register  for  the  Year  1761,  .  .  .  .  521 
ART.  VIII.  Containing  a  short  Account  of  some  Observations 
of  the  Transit  of  Venus,  A.  D.  1761,  June  6th  ; 
and  the  Distance  of  the  Planets  from  the  Sun, 
9$  deduced  from  those  Observations*  -  »  52& 


CH  ^V 


ASTRONOMY  EXPLAINED. 

CHAP.  L 

Of  Astronomy  in  general* 

,     /~\F  all  the  sciences  cultivated  by  mankind,  ^ 

\^J  astronomy  is  acknowledged  to  be,  andastrono 
undoubtedly  is,  the  most  sublime,  the  most  inter-  my« 
esting,  and  the  most  useful.  For,  by  knowledge 
derived  from  this  sr.ieucc,  not  only  the  magnitude 
of  the  earth  is  discovered,  the  situation  and  extent 
of  the  countries  and  kingdoms  upon  it  ascertained, 
trade  and  commerce  carried  on  to  the  remotest 
parts  of  the  world,  and  the  various  products  of  se- 
veral countries  distributed  for  the  health,  comfort,, 
and  conveniency  of  its  inhabitants ;  but  our  very  fa- 
culties are  enlarged  with  the  grandeur  of  the  ideas 
it  conveys,  our  minds  exalted  above  the  low  con- 
tracted prejudices  of  the  vulgar,  and  our  under- 
standings clearly  convinced,  and  affected  with  the 
conviction,  of  the  existence,  wisdom,  power,  good- 
ness, immutability,  and  superintendency  of  the 
SUPREME  BEING.  So  that,  without  an  hy- 
perbole, 

"  An  unde-vout  astronomer  is  mad.*" 

2.  From  this  branch  of  knowledge  we  also  learn 
by  what  means  or  laws  the  Almighty  carries  on, 
and  continues,  the  wonderful  harmony,  order,  and 
connexion,  observable  throughout  the  planetary 
system ;  and  are  led,  by  very  powerful  arguments^ 
to  form  this  pleasing  deduction — that  minds  capabk 

*  Dr.  Young's  Night  Thoughts* 

E 


32  Of  Astronomy  in  general. 

of  such  deep  researches,  not  only  derive  their  ori- 
gin from  that  adorable  Being,  but  are  also  incited 
to  aspire  after  a  more  perfect  knowledge  of  his  na- 
ture, and  a  stricter  conformity  to  his  will. 
The  Earth  3.  By  astronomy,  we  discover  that  the  Earth  is 
asUtseePn°mt  at  so  §reat  a  distance  from  the  Sun,  that  it  seen  from 
from  the  thence  it  would  appear  no  larger  than  a  point ;  al- 
Surt'  though  its  circumference  is  known  to  be  25,020 
miles.  Yet  even  this  distance  is  so  small,  compared 
with  that  of  the  fixed  stars,  that  if  the  orbit  in  which 
the  Earth  moves  round  the  Sun  were  solid,  and  seen 
from  the  nearest  star,  it  would  likewise  appear  no 
larger  than  a  point ;  although  it  is  about  162  mil- 
lions of  miles  in  diameter.  For  the  Earth,  in  go- 
ing round  the  Sun,  is  162  millions  of  miles  nearer 
to  some  of  the  stars  at  one  time  of  the  year,  than 
at  another ;  and  yet  their  apparent  magnitudes,  si- 
tuations and  distances  from  one  another,  still  re- 
main  the  same;  and  a  telescope  which  magnifies 
above  200  times,  does  not  sensibly  magnify  them. 
This  proves  them  to  be  at  least  400  thousand  times 
farther  from  us  than  we  are  from  the  Sun. 

4.  It  is  not  to  be  imagined  that  all  the  stars  are 
placed  in  one  concave  surface,  so  as  to  be  equally 
distant  from  us ;  but  that  they  are  placed  at  im- 
mense  distances  from   one  another,  through  unli- 
mited space.     So  that  there  may  be  as  great  a  dis- 
tance between  any  two  neighbouring  stars,  as  be- 
tween the  Sun  and  those  which  are  nearest  to  him. 
An  observer,  therefore,  who  is  nearest  any  fixed 

The  stars  star,  will  look  upon  it  alone  as  a  real  Sun ;  and  con- 
are  aims,  sjcjer  t}ie  rest  as  so  many  shining  points,  placed  at 

equal  distances  from  him  in  the  firmament. 

5.  By  the  help  of  telescopes  we  discover  thousands 
of  stars  which  are  invisible  to  the  bare  eye;  and 
the  better  our  glasses  are,  still  the  more  stars  become 

and  innu-  visible :  so  that  we  can  set  no  limits  either  to  their 
number  or  tnejr  distances.  The  celebrated  HUY- 
GENS  carried  his  thoughts  so  far,  as  to  believe  it 
not  impossible  that  there  may  be  stars  at  such 


Of  Astronomy  In  general.  33 

inconceivable  distances,  that  their  light  has  not  yet 
reached  the  Earth  since  its  creation;  although  the 
velocity  of  light  be  a  million  of  times  greater  than 
the  velocity  of  a  cannon-ball,  as  shall  be  demon- 
strated aiu  I  \-.ard,  \  197.216. — And,  as  Mr.  AD- 
DISON  very  justly  observes,  this  thought  is  far  from 
being  extravagant,  when  we  consider  that  the  uni- 
verse is  the  work  of  infinite  power,  prompted  by  in- 
finite goodness ;  having  an  infinite  space  to  exert  it- 
self in ;  so  that  our  imaginations  can  set  no  bounds 
to  it. 

6t   The  Sun  appears  very  bright  and  large  in  Why  the 
comparison  with  the  fixed  stars,  because  we  keep  j^arsapfar- 
constantly  near  the  Sun,   in  comparison  with  our  ger  than 
immense  distance  from  the  stars.     For,  a  spectator the  sUr-?* 
placed  as  near  to  any  star  as  we  are  to  the  Sun, 
would  see  that  star  a  body  as  large  and  bright  as 
the  Sun  appears  to  us :  and  a  spectator  as  far  distant 
from  the  sun  as  we  are  from  the  stars,  would  see 
the  Sun  as  small  as  we  see  a  star,  divested  of  all  its 
circumvolving  planets ;  and  would  reckon  it  one  of 
the  stars  in  numbering  them.  ^ 

7.  The  stars,  being  at  such  immense  distances  Tbe  stAs 
from  the  Sun,  cannot  possibly  receive  from  him  sof.re"ote? 

%  ,    .   ,      lightened 

strong  a  light  as  they  seem  to  have ;  nor  any  bright*  by  the 
ness  sufficient  to  make  them  visible  to  us.  For  the  Sun- 
Sun's  rays  must  be  so  scattered  and  dissipated 
before  they  reach  such  remote  objects,  that  they 
can  never  be  transmitted  back  to  our  eyes,  so  as  to 
render  these  objects  visible  by  reflection.  The  stars 
therefore  shine  with  their  own  native  and  unbor- 
rowed  lustre,  as  the  Sun  does.  And  since  each  par- 
ticular star,  as  well  as  the  Sun,  is  confined  to  a  par- 
ticular portion  of  space,  it  is  plain  that  the  stars  are 
of  the  same  nature  with  the  Sun. 

8.  It  is  no  ways  probable  that  the  Almighty, 
who  always  acts  with  infinite  wisdom,  and  does  no- 
thing in  vain,  should  create  so  many  glorious  suns, 
fit  for  so  many  important  purposes,  and  place  them 
.at  such  distances  from  one  another,   without  pro- 


34  Of  Astronomy  in  general. 

per  objects  near  enough  to  be  benefited   by  their 
They  are  influence.  Whoever  imagines  that  they  were  created 
summnd-  only  to  give  a  faint  glimmering  light  to  the  inha- 
e<]  by  pia-  bitants  of  this  globe,  must  have  a  very  superficial 
knowledge  of  astronomy,  and  a  mean  opinion  of  the 
Divine  Wisdom :  since,  by  an  infinitely  less  exer- 
tion of  creating  power,  the  Deity  could  have  given 
our  Earth  much  more  li^ht  by  one  single  additional 
moon. 

9.  Instead  then  of  one  Sun  and  one  world  only 
in  the  universe,  as  the  unskilful  in  astronomy  ima- 
gine, that  science  discovers  to  us  such  an  incon- 
ceivable number  of  suns,  systems,  and  worlds,  dis- 
persed through  boundless  space,  that  if  our  Sun, 
with  all  the  planets,  moons,  and  comets,  belonging 
to  it,  were  annihilated,  they  would  be  no  more 
missed,  by  an  eye  that  could  take  in  the  whole 
creation,  than  a  grain  of  sand  from  the  sea-shore — 
the  space  they  possess  being  comparatively  so  small, 
that  it  would  scarce  be  a  sensible  blank  in  the  uni- 
verse. Saturn,  indeed,  the  outermost  of  our  plan- 
cts,  revolves  about  the  Sun  in  an  orbit  of  4884  mil- 
lions of  miles  in  circumference  ;*•  and  some  of  our 
comets  make  excursions  upwards  of  ten  thousand 
millions  of  miles  beyond  Saturn's  orbit ;  and  yet, 
at  that  amazing  distance,  they  are  incomparably 
nearer  to  the  Sun  than  to  any  of  the  stars.  This  is 
evident  from  their  keeping  clear  of  the  attractive 
power  of  all  the  stars,  and  returning  periodically  by 
virtue  of  the  Sun's  attraction. 

The  stei-       ]_().  From  what  we  know  of  our  own  system,  it 
may beha- mav  be  reasonably  concluded  that  all  the  rest  are 
4ntable,     with   equal    wisdom   contrived,    situate,    and   pro- 
vided  with  accommodations   for   rational    inhabit- 
ants.     Let  us  therefore    take    a    survey    of   the 
system  to  which  we  belong,  the  only  one  accessi- 
ble to  us,  and  from  thence  we  shall  be  the  better 

*  The  Georgian  planet,  discovered  since  Mr.  Ferguson's  time,  re- 
volves round  the  Sun  in  an  orbit  5673  millions  of  miles  in  circumfer- 
ence, 


Of  Astronomy  in  general.  35 

enabled  to  judge  of  the  nature  and  end  of  the  other 
systems  of  the  universe.  For,  although  there  is  an 
almost  infinite  variety  in  the  parts  of  the  creation, 
whicli  we  have  opportunities  of  examining,  yet  there 
is  a  general  analogy  running  through  and  connecting 
all  the  parts  into  one  scheme,  one  design,  one  whole. 

11.  And  then,  to  an  attentive  considerer,  it  will 
appear  highly  probable,  that  the  planets  of  our  sys- 
tem, together  with  their  attendants  called  satellites 
or  moons,  are  much  of  the  same  nature  with,  our 
Earth,  and  destined  for  the  like  purposes.     They 
are  all  solid  opaque  globes,  capable  of  supporting  are. 
animals  and  vegetables.     Some  of  them  are  larger, 
some  less,  and  some  nearly  of  the  same  size  of  our 
Earth.     They  all  circulate  round  the  Sun,  as  the 
Earth  does,  in  shorter  or  longer  times,  according  to 
their  respective  distances  from  him  ;  and  have,  where 

it  would  not  be  inconvenient,  regular  returns  of  sum- 
mer and  winter,  spring  and  autumn.  They  have 
warmer  and  colder  climates,  as  the  various  produc- 
tions ot  our  Earth  require  :  and  in  such  as  afford  a 
possibility  of  discovering  it,  we  observe  a  regular 
motion  round  their  axes  like  that  of  our  Earth,  caus- 
ing an  alternate  return  of  day  and  night ;  which  is 
necessary  for  labour,  rest,  and  vegetation ;  and  that 
all  parts  of  their  surfaces  may  be  alternately  exposed 
to  the  rays  of  the  Sun. 

12.  Such  of  the  planets  as  are  farthest  from  theThefar- 
Sun,  and  therefore  enjoy  least  of  his  light,  have  thattj)e  sun 
deficiency  made  up  by  several  moons,  which  con-  have  most 
stantly  accompany,  and  revolve  about  them  ;  as  our^j?^^ 
Moon  revolves  about  the   Earth.     The   remotest  their 
planet*  has,  over  and  above,  a  broad  ring  encom-  ni£hts- 
passing  it ;  which,  like  a  lucid  zone  in  the  heavens, 
reflects  the  Sun's  light  very  copiously  on  that  planet: 

so  that  if  the  remoter  planets  have  the  Sun's  light 
fainter  by  day  than  our  earth,  they  have  an  addition 
rrjiade  to  it  morning  and  evening  by  one  or  more  of 

is  now  known  to.havc  two  of  these  lucid  zones  or  ring)?. 


36  Of  Astronomy  in  general. 

Our  Moon  their  moons,  and  a  greater  quantity  of  light  in  the 


the  Earth.  13.  On  the  surface  of  the  Moon,  because  it  is 
nearer  to  us  than  any  other  of  the  celestial  bodies 
are,  we  discover  a  nearer  resemblance  of  our  Earth. 
For,  by  the  assistance  of  telescopes,  we  observe  the 
Moon  to  be  full  of  high  mountains,  large  vallies, 
and  deep  cavities.  These  similarities  leave  us  no 
room  to  doubt,  that  all  the  planets  and  moons  in  the 
system,  are  designed  as  commodious  habitations  for 
creatures  endowed  with  capacities  of  knowing  and 
adoring  their  beneficent  Creator. 

14.  Since  the  fixed  stars  are  prodigious  spheres 
of  fire  like  our  Sun,*  and  at  inconceivable  distances 
from  one  another,  as  well  as  from  us,  it  is  reasona- 
ble to  conclude,  they  are  made  for  the  same  pur- 
poses that  the  Sun  is ;  each  to  bestow  light,  heat,  and 
vegetation  on  a  certain  number  of  inhabited  planets ; 
kept  by  gravitation  within  the  sphere  of  its  activity. 

Number-       ]^  What  an  august,  whan  an  amazing  concep- 

less  suns      .  .P    ,  .    •  5    .        .  .     ° .  * 

and  tion,  if  human  imagination  can  conceive  it,  does 
worlds,  this  give  of  the  works  of  the  Creator  !  Thousands 
of  thousands  of  suns,  multiplied  without  end,  and 
ranged  all  around  us,  at  immense  distances  from  each 
other ;  attended  by  ten  thousand  times  ten  thousand 
worlds,  all  in  rapid  motion,  yet  calm,  regular,  and 
harmonious,  invariably  keeping  the  paths  prescribed 
them ;  and  these  worlds  peopled  with  myriads  of  in- 
telligent beings,  formed  for  endless  progression  in 
perfection  and  felicity ! 

16.  If  so  much  power,  wisdom,  goodness,  and 
magnificence  be  displayed  in  the  material  creation, 
which  is  the  least  considerable  part  of  the  universe, 
how  great,  how  wise,  how  good,  must  HE  BE, 
who  made  and  governs  the  whole ! 

*  Though  the  Sun  may  not,  strictly  speaking,  be  a  great  sphere  of 
fire,  yet  it  is  undoubtedly  the  principal  source  of  light  and  heat  to  the 
other  bodies  in  the  system. 


Of  the  Solar  System 


CHAP.  II. 


A  brief  Description  of  the  SOLAR  SYSTEM. 


Sun,  with  the  planets  and  comets  £[*'*/' 
which  move  round  him  as  their  centre, 
constitute  the  solar  system.  Those  planets  which 
are  near  the  Sun  not  only  finish  their  circuits  sooner, 
but  likewise  move  faster  in  their  respective  orbits, 
than  those  which  are  more  remote  from  him.  Their 
motions  are  all  performed  from  west  to  east,  in  orbits 
nearly  circular.  Their  names,  distances,  magni- 
tudes, and  periodical  revolutions,  are  as  follows  : 

18.  The  Sun  0  ,  an  immense  globe  of  fire,  isThcSun 
placed  near  'the  common  centre,  or  rather  in  the 
lower*  focus  of  the  orbits  of  all  the  planets  and  co- 
metsf  ;  and  turns  round  his  axis  in  25  days  6  hours, 
as  is  evident  by  the  motion  of  spots  seen  on  his  sur- 
face.    His   diameter  is  computed  to   be   76  3  ,000  ^ff-1? 
miles  ;  and  by  the  various  attractions  of  the  circum- 
volving  planets,  he  is  agitated  by  a  small  motion 

*  If  the  two  ends  of  a  thread  be  tied  together,  and  die  thread  be 
then  thrown  loosely  round  two  pins  stuck  in  a  table,  and  moderately 
stretched  by  the  point  of  a  black-lead  pencil  carried  round  by  an 
even  motion,  and  light  pressure  of  the  hand,  and  oval  or  ellipsis  will 
be  described  ;  and  the  points  where  the  pins  are  fixed  are  called  the 
foci  or  focuses  of  the  ellipsis.  The  orbifs  of  all  the  planets  are  ellip- 
tical, and  the  Sun  is  placed  in  or  near  one  of  the  foci  of  each  of  them  : 
and  that  in  which  he  is  placed,  is  called  the  lower  focus* 

t  Astronomers  are  not  far  from  the  truth  when  they  reckon  the 
Sun's  centre  to  be  in  the  lower  focus  of  all  the  planetary  orbits. 
Though,  strictly  speaking,  if  we  consider  the  focus  of  Mercury's 
orbit  to  be  in  the  Sun's  centre,  the  focus  of  Venus's  orbit  will  be  in 
the  common  centre  of  gravity  of  the  Sun  and  Mercury  ;  the  focus 
of  the  Earth's  orbit  in  the  common  centre  of  gravity  of  the  Sun, 
Mercury,  and  Venus  ;  the  focus  of  the  orbit  of  Mars  in  the  com- 
mon centre  of  gravity  of  the  Sun,  Mercury,  Venus,  and  the  Earth; 
and  so  of  the  rest.  Yet  the  focuses  of  the  orbits  of  all  the  planets, 
except  Saturn,  will  not  be  sensioly  removed  from  the  centre  of  the 
Sun  ;  nor  will  the  focus  of  Saturn's  orbit  recede  sensibly  from  the 
common  centre  of  gravity  of  the  Sun  and  Jupiter, 


38  Of  the  Solar  System*. 

Plate  I.  round  the  centre  of  gravity  of  the  system.  All  the 
planets,  as  seen  from  him,  move  the  same  way,  and 
according  to  the  order  of  the  signs  in  the  graduated 
circle  T  tf  n  s,  fcfr.  which  represents  the  great 
ecliptic  in  the  heavens :  but,  as  seen  from  any  one 
planet,  the  rest  appear  sometimes  to  go  back  ward  ? 
sometimes  forward,  and  sometimes  to  stand  still. 
These  apparent  motions  are  not  in  circles  nor  in  el- 
lipses, but*  in  looped  curves,  which  never  return 
into  themselves.  The  comets  come  from  all  parts 
of  the  heavens,  and  move  in  all  directions. 

19.  Having  mentioned  the  Sun's  turning  round 

his  axis,  and  as  there  will  be  frequent  occasion  to 

speak  of  the  like  motion  of  the  Earth  and  other 

planets,  it  is  proper  here  to  inform  the  young  Tyro 

in  astronomy,  that  neither  the  Sun  nor  planets  have 

material  axes  to  turn  upon,  and  support  them,  as 

The  axes  in  the  little  imperfect  machines  contrived  to  repre- 

netsT  pla" sent  them.     For  the  axis  of  a  planet  is  an  imginary 

what.       line,    conceived  to   be   drawn   through    its  centre, 

about  which  it  revolves  as  if  on  a  real  axis.     The 

extremities   of  this  axis,   terminating   in   opposite 

points  of  the  planet's  surface,  are  called  its  poles. 

That  which  points  toward  the  northern  part  of  the 

heavens,  is  called  the  north  pole ;  and  the  other, 

pointing  toward  the  southern  part,  is  called  the  south 

pole.  A  bowl  whirled  from  one's  hand  into  the  open 

air,  turns  round  such  a  line  within  itself,  while  it 

moves  forward ;  and  such  are  the  lines  we  mean, 

when  we  speak  of  the  axes  of  the  heavenly  bodies. 

Their  or-      20.  Let  us  suppose  the  Earth's  orbit  to  be  a  thin, 

notbtthe  even>  solid  Plane  >  cutting  the  Slln  through  the  cen- 

same        tre,  and  extended  out  as  far  as  the  starry  heavens, 

P^j:lth  where  it  will  mark  the  great  circle  called  the  ecliptic. 

tic.          This   circle   we   suppose   to   be   divided   into    12 

equal  parts,  called  signs ;  each  sign  into  30  equal 

parts,  called  degrees;   each  degree  into   60   equal 

parts,   called   minutes;   and  each  minute   into   60 

*  As  represented  in  Plate  III.  Fig.  I.  and  described  $  138, 


Of  the  Solar  System.  39 

into  60  equal  parts,  called  seconds :  so  that  a  second  Platt  f. 
is  the  60th  part  of  a  minute ;  a  minute  the  60th 
part  of  a  degree ;  and  a  degree  the  360th  part  of 
a  circle,  or  ijOth  part  of  a  sign.     The  planes  of 
the  orbits  of  all  the  other  planets  likewise  cut  the 
Sun  in  halves ;  but,  extended  to  the  heavens,  form 
circles   different  from   one  another,    and  from  the 
ecliptic  ;  one  half  of  each  being  on  the  north  side, 
and  the  other  on  the  south  side  of  it.     Consequent-  Their 
ly  the  orbit  of  each  planet  crosses  the  ecliptic  in  two  node8' 
opposite  points,  which  are  called  the  planets'  nodes. 
These  nodes  are  all  in  different  parts  of  the  ecliptic ; 
and  therefore,  if  the  planetary  tracks  remained  vi- 
sible in  the  heavens,  they  would  in  some  measure 
resemble  the  different  ruts  of  waggon  wheels,  cross- 
Ing  one  another  in  different  parts,  but  never  going 
far  asunder*     That  node,  or  intersection  of  the  or- 
bit of  any  planet  with  the  Earth's  orbit,  from  which 
the  planet  ascends  northward  above  the  ecliptic,  is 
called  the  ascending  node  of  the  planet :  and  the  other, 
which  is  directly  opposite  thereto,  is  called  its  de- 
scending node.     Saturn's  ascending  node*  is  in  21  Where  si- 
deg.  32  min.  of  Cancer  25  ;  Jupiter's  in  8  deg.  49 tuate- 
min.  of  the  same  sign;  Mars's  in  18  deg.  22  min. 
of  Taurus  tf  ;  Venus's  in  14  deg.  44  min.  of  Ge- 
mini n  ;  and  Mercury's  in  16  deg.  2  min.  of  Taurus. 
Here  we  consider  the  Earth's  orbit  as  the  stand- 
ard, and  the  orbits  of  all  the  other  planets  as  ob- 
lique to  it. 

21.  When  we  speak  of  the  planets'  orbits,  all  that  The  plan- 
is  meant  is,  their  paths  through  the  open  and  unre-  ets»  orbits, 
sisting  space  in  which  they  move,  and  are  retained  what' 
by  the  attractive  power  of  the  Sun,  and  the  pro- 
jectile force  impressed  upon  them  at  first.     Between 
this  power  and  force  there  is  so  exact  an  adjustment, 
that  they  continue  in  the  same  tracks  without  any- 
solid  orbits  to  confine  them. 

*  In  the  year  1790. 

F 


40  Of  the  Solar  System. 

Plate  i.        22.  MERCURY,  the  nearest  planet  to  the  Sun, 
Mercury   ^^^  round  him,  in  the  circle  marked  8,  in  87  days, 
ri£-  I-      23  hours  of  our  time,  nearly;  which  is  the  length  of 
his  year.     But  being  seldom  seen,   and  no  spots 
appearing  on  his  surface  or  disc,  the  time  of  his  ro- 
tation on  his  axis,  or  the  length  of  his  days  and 
nights  is  as  yet  unknown.     His  distance  from  the 
Sun  is  computed  to  be  32  millions  of  miles,  and  his 
diameter  2600.     In  his  course  round  the  Sun,  he 
moves  at  the  rate  of  95  thousand  miles  every  hour. 
His  light  and  heat  from  the  Sun  are  almost  seven 
times  as  great  as  ours ;  and  the  Sun  appears  to  him 
May  be  in- almost  seven  times  as  large  as  to  us.     The  great 
habited.    j^  Qn  tj^g  pjanet  js  no  argument  against  its  being 

inhabited ;  since  the  Almighty  could  as  easily  suit 
the  bodies  and  constitutions  of  its  inhabitants  to  the 
heat  of  their  dwelling,  as  he  has  done  ours  to  the 
temperature  of  our  Earth.  And  it  is  very  probable 
that  the  people  there  have  just  such  an  opinion  of  us, 
as  we  have  of  the  inhabitants  of  Jupiter  and  Saturn ; 
namely,  that  we  must  be  intolerably  cold,  and  have 
very  little  light,  at  so  great  a  distance  from  the  Sun. 
Has  like  23.  This  planet  appears  to  us  with  all  the  vari- 
withThe  ous  phases  of  the  Moon,  when  viewed  at  different 
Moon.  times  by  a  good  telescope  :  save  only,  that  he  never 
appears  quite  full,  because  his  enlightened  side  is 
never  turned  directly  toward  us,  but  when  he  is  so 
near  the  Sun  as  to  be  lost  to  our  sight  in  its  beams. 
And,  as  his  enlightened  side  is  always  toward  the 
Sun,  it  is  plain  that  he  shines  not  by  any  light  of 
his  own  ;  for  if  he  did,  he  would  constantly  appear 
round.  That  he  moves  about  the  Sun  in  an  orbit 
within  the  Earth's  orbit,  is  also  plain  (as  will  be 
more  largely  shewn  by  and  by,  §  141,  &  seq.J  be- 
cause he  is  never  seen  opposite  to  the  Sun,  nor  in- 
deed above  56  times  the  Sun's  breadth  from  his 
centre. 


Of  the  Solar  System.  41 


24.  His  orbit  is  inclined  seven  degrees  to 
ecliptic.      That  node,  §20,  from  which  he  ascends 
northward  above  the  ecliptic,  is  in  the   16th  degree 
of  Taurus  ;  and  the  opposite  node,  in  the  16th  de- 
gree of  Scorpio.     The  Earth  is  in  these  points  on 
the  7th  of  November  and  5th  of  May\  and  when 
Mercury  comes  to  either  of  his  nodes  at  his*  infe- 
rior conjunction  about  these  times,  he  will  appear  to 
pass  over  the  disc  or  face  of  the  Sun,  like  a  dark 
round  spot.     But  in  all  other  parts  of  his  orbit  his 
conjunctions  are  invisible;  because  he  either  passes 
above  or  below  the  Sun. 

25.  Mr.  WHISTON   has  given  us  an  account  of  when 
several  periods  at  which  Mercury  might  be  seen  on  ^Leonn  JjJ 
the  Sun's  disc,  viz.  In  the  year  17fc2,  Nov.  12th,  sun. 

at  3  h.  44  m.  in  the  afternoon,  1786,  May  4th,  at 
6  h.  57  m.  in  the  forenoon  ;  1789,  Nov.  5th,  at  3 
h.  55  m.  in  the  afternoon  ;  and  1799,  May  7th,  at 
2  h.  34m.  in  the  afternoon.  There  were  several 
intermediate  transits,  but  none  of  them  visible  at 
London. 

26.  VENUS,  the  next  planet  in  order,  is  com-  Venus. 
puted  to  be  59  millions  of  miles  from  the  Sun; 

and  by  moving  at  the  rate  of  69  thousand  miles 
every  hour,  in  her  orbit  in  the  circle  marked  9  ,  she  Fig.  i: 
goes  round  the  Sun  in  224  days,  17  hours  of  our 
time,  nearly  ;  in  which,  though  it  be  the  full 
length  of  her  year,  she  has  only  91  days,  accord- 
ing toBiANCHiNi's  observations'!*  ;  so  that,  to  her, 

*  When  he  is  between  the  Earth  and  the  Sun  in  the  nearest  part 
of  his  orbit. 

t  The  elder  Cassini  had  concluded  from  observations  made  by 
himself  in  1667,  thnt  Venus  revolved  on  her  axis  in  a  little  more 
than  23  h.  because  in  24  h.  he  found  that  a  spot  on  her  surface  was 
about  15°  more  advanced  than  it  was  at  the  day  before  ;  and  it  ap- 
peared to  him  that  the  spot  was  very  sensibly  advanced  in  a  quar- 
ter of  an  hour.  In  1728,  Bianchini  published  a  splendid  work,  in 
folio,  at  Rome,  entitled  Hesfieri  et  Phosfihori  nova  fihanomena; 
in  which  are  the  observations  here  referred  to.  Bianchini  agrees 


42  Of  the  Solar  System. 

Plate  I.  every  clay  and  night  together  is  as  long  as  24-|  days 
and  nights  with  us.  This  odd  quarter  of  a  c'av  in 
every  year  makes  every  fourth  a  leap-year  to  Vtuiis ; 
as  the  like  does  to  our  Earth.  Her  dmmt-ter  is  7906 
miles;  and  by  her  diurnal  motion  the  inhabitants 
about  her  equator  are  carried  43  miles  every  hour, 
beside  the  69,000  above-mentioned. 

Her  orbit      27.  Her  orbit  includes  that  ot  Mercury  within 
tween  the  ^  5  f°r  at  ^er  greatest  elongation,  or  apparent  dis- 
Earth  andtance  from  the  Sun,  she  is  96  times  the  breadth  of 
Mercury.  ^^   iummary   frorn   his  centre ;   which   is  almost 
double  of  Mercury's  greatest  elongation.     Her  or- 
bit is  included  by  the  Earth's ;  for  ii  it  were  not, 
she  might  be  seen  as  often  in  opposition  to  the  Sun, 
as  she  is  in  conjunction  with  him ;  but  she  has  ne- 
ver been  seen  90  degrees,  or  a  fourth  part  of  a  circle 
from  the  Sun. 

She  is  our     28.  When  Venus  appears  west  of  the  Sun,  she 
ImTeven-  r*ses  before  him  in  the  morning,  and  is  called  the 
ing  slur  by  morning  star:  when  she  appears  east  of  the  Sun, 
turns.       she  shines  in  the  evening  after  he  sets,  and  is  then 
called  the  evening  star:    being  each  in   its    turn 
for  290   days.     It   may   perhaps  be  surprising  at 
first  view,  that  Venus  should  keep  longer  on  the  east 
or  west  of  the  Sun,  than  the  whole  time  of  her  pe- 
riod round  him.     But  the  difficulty  vanishes  when 
we  consider  that  the  Earth  is  all  the  while  going 
round  the  Sun  the  same  way,  though  not  so  quick 
as  Venus  :  and  therefore  her  relative  motion  to  the 

perfectly  with  Cassini  that  the  spots,  which  are  seen  on  the  surface 
of  Venus,  advance  about  15°  in  24  h.  but  he  asserts  that  he  could 
not  perceive  they  had  made  any  advance  in  3  h.  and  therefore  con- 
dudes  that  instead  of  making  one  complete  revolution  and  15°  of  an- 
other, as  Cassini  conjectured,  in  24  h.  those  spots  advance  but  the  odd 
15°  in  that  time,  and  that  the  time  of  a  revolution  is  somewhat  more 
than  24  days.  The  arguments  in  favour  of  the  two  hypothv  ses  are 
very  equal ;  but  almost  every  astronomer,  except  Mr.  Ferguson* 
has  adopted  Cassini's. 


Of  the  Solar  System.  43 

Earth  must  in  every  period  be  as  much  slower  than 
her  absolute  motion  in  her  orbit,  as  the  Earth  du- 
ring that  time  advances  forward  in  the  ecliptic ; 
which  is  220  degrees.  To  us  she  appears,  through 
a  telescope,  in  all  the  various  shapes  of  the  moon. 

29.  The  axis  of  Venus  is  inclined  75  degrees  to 
the  axis  of  her  orbit;  which  is  51*  degrees  more 
than  our  Earth's  axis  is  inclined  to  the  axis  of  the 
ecliptic  :  and  therefore  her  seasons  vary  much  more 
than  ours  do.     The  north  pole  of  her  axis  inclines 
toward  the  20th  degree  of  Aquarius ;  our  Earth's 
to    the    beginning   of    Cancer ;    consequently  the 
northern  parts  of  Venus  have  summer  in  the  signs 
where  those  of  our  Earth  have  winter,  and  vice 
-versa. 

30.  The*  artificial  day  at  each  pole  of  Venus  is  Remark- 
as  long  as  ll^lf  natural  days  on  our  Earth.  pelranPces. 

31.  The  Sun's  greatest  declination  on  each  side  Her  tro-  ' 
of  her  equator  amounts  to  75  decrees ;  therefore  Pi(rs  an.d 

,  t  polar  cir- 

herj  tropics  are  only  15  degrees  from  her  poles ;  cks  how 
and  her ]|  polar  circles  are  as  far  from  her  equator,  situate. 
Consequently  the  tropics  of  Venus  are  between  her 
polar  circles  and  her  poles ;  contrary  to  what  those 
of  our  Earth  are. 

32.  As  her  annual  revolution  contains  only  9.*  The  Sun's 
of  her  days,  the   Sun   will  always   appear  to   godaily 
through   a    whole   sign,    or  twelfth    part    of   rierc° 
orbit,   in  a  little  more  than  three  quarters  of  her 

*  The  time  between  the  Sun's  rising  and  setting. 

t  One  entire  revolution,  or  24  hours. 

\  These  are  lesser  circles  parallel  to  the  equator,  and  as  many 
degrees  from  it,  toward  the  poles,  as  the  axis  of  the  planet  is  inclined 
to  the  axis  of  its  orbit.  When  the  Sun  is  advanced  so  far  north  or 
south  of  the  equator,  as  to  be  directly  over  either  tropic,  he  goes  no 
farther ;  but  returns  toward  the  other. 

||  These  are  lesser  circles  round  the  poles,  and  as  far  from  them 
as  the  tropics  are  from  the  equator.  The  poles  are  the  very  north 
and  south  points  of  the  planet. 


44 


Of  the  Solar  System. 


natural   day,    or  nearly   in  18|   of   our  days    and 
nights. 

33'  Because  her  da>" is  so  great  a  P^*  of  her  year, 
.  the  Sun  changes  his  declination  in  one  day  so  mi:  hu 
that  if  he  passes  vertically,  or  directly  over  fctaci  of 
any  given  place  on  the  tropic,  the  next  day  he  will 
be  26  degrees  from  it ;  and  whatever  place  he  passes 
vertically  over  when  in  the  Equator,  one  day's  re- 
volution will  remove  him  36|  degrees  from  it.  So 
that  the  Sun  changes  his  declination  e%very  day  in 
Venus  about  14  degrees  more,  at  a  mean  rate,  than 
he  does  in  a  quarter  of  a  year  on  our  Earth.  This 
appears  to  be  providentially  ordered,  for  preventing 
the  too  great  effects  of  the  Sun's  heat,  (which  is 
twice  as  great  on  Venus  as  on  the  Earth,)  so  that 
he  cannot  shine  perpendicularly  on  the  same  places 
for  two  days  together;  and  on  that  account,  the 
heated  places  have  time  to  cool 

To  deter-       34.  if  the   inhabitants  about  the  north   pole  of 

po'mts  of    ^  enus  lix  their  south,  or  meridian  line,  through  that 

the  com-  part  of  the  heavens  where  the  Sun  comes  to  his 

her5 poles.  greatest  height,  or  north  declination,  and  call  those 

the  east  and  west  points  of  their  horizon,  which  are 

90  degrees  on  each  side  from  that  point  where  the 

horizon  is  cut  by  the  meridian  line,  these  inhabitants 

will  have  the  following  remarkable  appearances — 

The  Sun  will  rise  22|  degrees  north  of  the 
cast,  and  going  on  112|  degrees,  as  measured  on 
the  plane  of  the*  horizon,  he  will  cross  the  me- 
ridian at  an  altitude  of  12|-  degrees ;  then  making 
an  entire  revolution  without  setting,  he  will  cross 
it  again  at  an  altitude  of  48|  degrees.  At  the 
next  revolution  he  will  cross  the  meridian  as  he 
comes  to  his  greatest  height  and  declination,  at  the 

*  The  limit  of  any  inhabitant's  view,  where  the  sky  seems  tr, 
touch  the  planet  all  raund  him. 


Of  the  Solar  System.  45 

altitude  of  75  degrees  ;  being  then  only  15  degrees 
from  the  zenith*  or  that  point  of  the  heavens  which 
is  directly  over  head :  and  thence  he  will  descend  in 
the  like  spiral  manner,  crossing  the  meridian  first  at 
the  altitude  of  48*.  degrees,  next  at  the  altitude  of 
12|  degrees  ;  and  going  on  thence  lli^  degrees,  he 
will  set  22|  degrees  north  of  the  west.  So  that,  af- 
ter having  made  4|  revolutions  above  the  horizon, 
he  descends  below  it  to  exhibit  the  like  appearances 
at  the  south  pole. 

35.  At  each  pole,  the  Sun  continues  half  a  year  Surpris- 
without  setting  in   summer,  and  as   long  without 
rising  in  winter ;  consequently  the  polar  inhabitants  at  her 
of  Venus  have  only  one  day  and  one  night  in  thepoles" 
year ;  as  it  is  at  the  poles  of  our  earth.     But  the 
difference  between  the  heat  of  summer  and  cold  of 
winter,  or  of  mid-day  and  mid-night,  on  Venus, 

is  much  greater  than  on  the  Earth :  because  on  Ve- 
nus, as  the  Sun  is  for  half  a  year  together  above  the 
horizon  of  each  pole  in  its  turn,  so  he  is  for  a  con- 
siderable part  of  that  time  near  the  zenith  ;  and  du- 
ring tne  other  half  of  the  year  always  below7  the  ho- 
rizon, and  for  a  great  part  of  that  time  at  least  70 
degrees  from  it.  Whereas,  at  the  poles  of  our 
Earth,  although  the  Sun  is  for  half  a  year  together 
above  the  horizon ;  yet  he  never  ascends  above,  nor 
descends  below  it,  more  than  23?  degrees.  When 
the  Sun  is  in  the  equinoctial,  he  is  seen  with  one  half 
of  his  disc  above  the  horizon  of  the  north  pole,  and 
the  other  half  above  the  horizon  of  the  south  pole ; 
so  that  his  centre  is  in  the  horizon  of  both  poles : 
and  then  descending  below  the  horizon  of  one,  he 
ascends  gradually  above  that  of  the  other.  Hence, 
in  a  year,  each  pole  has  one  spring,  one  autumn,  a 
summer  as  long  as  them  both,  and  a  winter  equal  in 
length  to  the  other  three  seasons. 

36.  At  the  polar  circles  of  Venus,  the  seasons  At  Lfirpo- 

J*r  circles. 


46  Of  the  Solar  System. 

are  much  the  same  as  at  the  equator,  because  there 
are  only  15  degrees  between  them,  $  31;  only  the 
winters  are  not  quite  so  long,  nor  the  summers  so 
short :  but  the  four  seasons  come  twice  round  every 
year. 

At  her  27.  At  Venus's  tropics,  the  Sun  continues  for 
about  fifteen  of  our  weeks  together  without  setting 
in  summer ;  and  as  long  without  rising  in  winter. 
While  he  is  more  than  15  degree  from  the  equator, 
he  neither  rises  to  the  inhabitants  of  the  one  tropic, 
nor  sets  to  those  of  the  other  ;  whereas,  at  our  ter- 
restrial tropics,  he  rises  and  sets  every  day  of  the 
year. 

38.  At  Venus's  tropics,  the  seasons  are  much 
the  same  as  at  her  poles ;  only  the  summers  are  a 
little  longer,  and  the  winters  a  little  shorter* 

At  her  39.  At  her  equator,  the  days  and  nights  are  al- 
ways of  the  same  length ;  and  yet  the  diurnal  and 
nocturnal  arches  are  very  different,  especially  when 
the  Sun's  declination  is  about  the  greatest :  for  then, 
his  meridian  altitude  may  sometimes  be  twice  as 
great  as  his  midnight  depression,  and  at  other  times 
the  reverse.  When  the  Sun  is  at  his  greatest  cle- 
clination,  either  north  or  south,  his  rays  are  as  ob- 
lique at  Venus's  equator,  as  they  are  at  London  on 
the  shortest  day  of  winter.  Therefore,  at  her  equa- 
tor there  are  two  winters,  two  summers,  two  springs, 
and  two  autumns  every  year.  But  because  the  -Sun 
stays  for  some  time  near  the  tropics,  and  passes  so 
quickly  over  the  equator,  every  winter  there  will  be 
almost  twice  as  long  as  summer :  the  four  seasons 
returning  twice  in  that  time,  which  consist  only  of 
9£  days. 

40.  Those  parts  of  Venus  which  lie  between 
the  poles  and  tropics,  between  the  tropics  and  polar 
circles,  and  also  between  the  polar  circles  and  equa- 
tor, partake  more  or  less  of  the  phenomena  of  those 
circles,  as  they  are  more  or  less  distant  from  them. 


Of  the  Solar  System.  4,7 

41.  From  the  quick  change  of  the  Sun's  declina-  Great  dif- 
tion  it  happens,  that  if  he  rises  due  east  on  any  clay,  [^Sun's* 
he  will  not  set  due  west  on  that  day,  as  with  us.  amplitude 

For  if  the  place  where  he  rises  due  east  be  on  the  at  ?isin£ 
.„  and  set- 

equator,  he  will  set  on  that  day  almost  west-north-  ting. 

west,  or  about  18|  degrees  north  of' the  west.  But 
if  the  place  be  in  45  degrees  north  latitude,  then 
on  the  day  that  the  Sun  rises  due  east  he  will  set 
north- west- by- west,  or  33  degrees  north  of  the  west. 
And  in  62  degrees  north  latitude,  when  he  rises  in 
the  east,  he  sets  not  in  that  revolution,  but  just 
touches  the  horizon  10  degrees  to  the  west  of  the 
north  point ;  and  ascends  again,  continuing  for  3-J 
revolutions  above  the  horizon  without  setting. 
Therefore  no  place  has  the  forenoon  and  afternoon 
of  the  same  day  equally  long,  unless  it  be  on  the 
equator,  or  at  the  poles. 

42.  The  Sun's  altitude  at  noon,   or  any  other  The  long- 
time of  the  day,  and  his  amplitude  at  rising  and  tVde  of 

J...  ..—  places  ea- 

setting,  being  very  different  at  places  on  the  same  Sny  found 
parallel  of  latitude,  according  to  the  different  longi- in  Venus- 
tudes  of  those  places,  the  longitude  will  be  almost 
as  easily  found  on  Venus,  as  the  latitude  is  found 
on  the  Earth.     This  is  an  advantage  we  can  never 
have,  because  the  daily  change  of  the  Sun's  decli- 
nation,   is   by  much  too  small  for  that  important 
purpose. 

43.  On  this  planet,  where  the  Sun  crosses  theHerequi- 
equator  in  any  year,  he  will  have  9  degrees  of  de-  ^quane? 
clination  from  that  place  on  the  same  day  and  hour  of  a  day 
next  year,  and  will  cross  the  equator  90  degrees  far- 

ther  to  the  west ;  which  makes  the  time  of  the  equi- 
nox  a  quarter  of  a  day  (or  about  six  of  our  days) 
later  every  year.  Hence,  although  the  spiral  in 
which  the  Sun's  motion  is  performed  be  of  the  same 
sort  every  year,  yet  it  will  not  be  the  very  same  ; 
because  the  Sun  will  not  pass  vertically  over  the 
same  places  till  four  annual  revolutions  are  finished, 

G 


48  Of  the  Solar  System. 

Every          44.  We  may  suppose  that  the  inhabitants  of  Ve- 
Sa?*teapnus  w^  ke  caremi to  add  a  day  to  some  particular 
3-&arta     part  of  every  fourth  year  ;  which  will  keep  the  same 
to  Venus.  seasons  to  the  same  days.     For,  as  the  great  annual 
change  of  the  equinoxes  and  solstices  shifts  the  sea- 
sons a  quarter  of  a  day  every  year,  they  would  be 
shifted  through  all  the  days  of  the  year  in  36  years. 
But  by  means  of  this  intercalary  day,  every  fourth 
year  will  be  a  leap-year ;  which  will  bring  her  time  to 
an  even  reckoningrand  keep  her  calendar  always  right, 
when  she     45.  Venus's  orbit  i«>  inclined  3  degrees  24  mi- 
pear^m     nutes  to  the  Earth's;  and  crosses  it  in  the  15th  de- 
the  Sun.    grees  of  Gemini  and  of  Sagittarius ;  and  therefore, 
when  the  Earth  is  about  these  points  of  the  ecliptic 
at  the  time  that  Venus  is  in  her  inferior  conjunction, 
she  will  appear  like  a  spot  on  the  Sun,  and  afford  a 
more  certain  method  of  finding  the  distances  of  all 
the  planets  from  the  Suo,  than  any  other  yet  known. 
But  these  appearances  happening  very  seldom,  will 
be  only  twice  visible  at  London  for  one  hundred  and 
ten  years  to  come.     The  first  time  will  be  in  1761, 
June  the  6th,  in  the  morning;  and  the  second  in  1769,. 
on  the  3d  of  Ju?te,  in  the  evening.     Excepting  such 
transits  as  these,  she  exhibits  the  same  appearances 
to  us  regularly  every  eight  years ;  her  conjunctions, 
elongations,  and  times  of  rising  and  setting,  being, 
very  nearly  the  same,  on  the  same  days  as  before, 
she  may       46.  Venus  may  have  a  satellite  or  moon,  al- 
moVon%i-  though  it  be  undiscovered  by  us.     This  will  not 
though     appear  very  surprising,,  if  we  consider  how  incon- 
veniently  we  are  placed  for  seeing  it.     For  its  en- 
lightened  side  can  never   be  fully   turned  toward 
us,  except  when  Venus  is  beyond  the  Sun ;  and 
then,  as  Venus  appears  but  little  larger  than  an  or- 
dinary star,  her  moon  may  be  too  small  to  be  per- 
ceived at  such  a  distance.  *  When  she  is  between  us 
and  the  Sun,  her  full  moon  has  its  dark  side  toward 
us ;  and  then  we  cannot  see  it  any  more  than  we 
can  our  own  moon  at  the  time  of  change.    When 


Of  the  Solar  System.  49 

Venus  is  at  her  greatest  elongation,  we  have  but  Plate  I, 
one  half  of  the  enlightened  side  of  her  full  moon 
toward  us ;  and  even  then  it  may  be  too  far  distant 
to  be  seen  by  us.  But  if  she  have  a  moon,  it  may 
certainly  be  seen  with  her  upon  the  Sun,  in  the  year 
1761;  unless  its  orbit  be  considerably  inclined  to 
the  ecliptic :  for  if  it  should  be  in  conjunction  or  op- 
position at  that  time,  we  can  hardly  imagine  that  it 
moves  so  slow  as  to  be  hid  by  Venus  all  the  six 
-hours  that  she  will  appear  on  the  Sun's  disc*. 

47.  The  EARTH  is  the  next  planet  above  Venus  The  Earth 
in  the  system.     It  is  82  millions  of  miles  from  the  Pip.  i. 
Sun,  and  goes  round  him,  in  the  circle  ©,  in  365 

days  5  hours  49  minutes,  from  any  equinox  or  sol- 
stice  to  the  same  again ;  but  from  any  fixed  star  to 
the  same  again,  as  seen  from  the  Sun,  in  365  days 
6  hours  and  9  minutes.:  the  former  being  the  length  its  diurnal 
of  the  tropical  year,  and  the  latter  lfoe  length  of  theJ^jJJJ"* 
sidereal.  It  travels  at  the  rate  of  58  thousand  miles  • 
every  hour;  which  motion,  though  120  times  swift- 
er than  that  of  a  cannon-ball,  is  little  more  than  half 
as  swift  as  Mercury's  motion  in  his  orbit.  The 
Earth's  diameter  is  7970  miles;  and  by  turning 
round  its  axis  every  24  hours,  from  west  to  east,  it 
causes  an  apparent  diurnal  motion  of  all  the  heaven- 
ly bodies,  from  east  to  west.  By  this  rapid  motion 
of  the  Earth  on  its  axis,  the  inhabitants  about  the 
equator  are  carried  1042  miles  every  hour,  while 
those  on  the  parallel  of  London  are  carried  only 
about  580;  besides  the  58  thousand  miles,  by  the 
annual  motion  above-mentioned,  which  is  common 
to  all  places  whatever. 

48.  The  Earth's  axis  makes  an  angle  of  23*.  de-  inclination 
grees  with  the  axis  of  its  orbit;  and  keeps  always °?it8 "^ 
the  same  oblique  direction ;    inclining  toward  the 

...  *  Both  her  transits  are  over  since  this  was  written,  and  no  satel- 
lite was  seen  with  Venus  on  the  bun's  disc. 


50  Of  the  Solar  System. 

same  fixed  star*  throughout  its  annual  course, 
which  causes  the  returns  of  spring,  summer,  au- 
tumn, and  winter ;  as  will  be  explained  at  large  in 
the  tenth  chapter. 

A  proof  of  49.  The  Earth  is  round  like  a  globe ;  as  appears, 
L  B7  its  shadow  in  eclipses  of  the  Moon ;  which 
shadow  is  always  bounded  by  a  circular  line ;  §  314. 
2.  By  our  seeing  the  masts  of  a  ship  while  the  hull 
is  hid  by  the  convexity  of  the  water.  3.  By  its  hav- 
ing been  sailed  round  by  many  navigators.  The 
hills  take  oft'  no  more  from  the  roundness  of  the 
Earth  in  comparison,  than  grains  of  dust  do  from 
the  roundness  of  a  common  globe, 
its  num.  50.  The  seas  and  unknown  parts  of  the  Earth  (by 
a  measurement  OI*  ^ie  best  maps)  contain  160  mil- 
lions  522  thousand  and  26  square  miles ;  the  inhab- 
ited parts  38  millions  990  thousand  569  :  Europe  4 
millions  456  thousand  and  65  ;  Asia  10  millions  768 
thousand  823;  Africa  9  millions  654  thousand  807; 
America  14  millions  1 10  thousand  874.  In  all,  199 
millions  512  thousand  595;  which  is  the  number  of 
square  miles  on  the  whole  surface  of  our  globe. 
The  pro-  51.  Dr.  LONG,  in  the  first  volume  of  his  Astro- 
portion  of  nomy  p.  168,  mentions  an  ingenious  and  easy  me- 

landand      ,      •/     r    r*     v  •         ,111 

Sea.  thod  of  finding  nearly  what  proportion  the  land 
bears  to  the  sea ;  which  is,  to  take  the  papers  of  a 
large  terrestrial  globe,  and  after  separating  the  land 
from  the  sea,  with  a  pair  of  scissars,  to  weigh  them 
carefully  in  scales.  This  supposes  the  globe  to  be 
exactly  delineated,  and  the  papers  all  of  equal  thick- 
ness. The  doctor  made  the  experiment  on  the  pa- 
pers of  Mr.  SEN  EX'S  seventeen  inch  globe;  and 
found  that  the  sea-papers  weighed  349  grains,  and 
the  land  only  124  :  by  which  it  appears  that  almost 

*  This  is  not  strictly  true,  as  will  appear  when  we  come  to  treat 
of  the  recession  of  the  equinoctial  points  in  the  heavens,  §  246 ;  which 
recession  is  equal  to  the  deviation  of  the  Earth's  axis  from  its  pa- 
rallelism ;  but  this  is  rather  too  small  to  be  sensible  in  an  age,  ex- 
cept to  those  who  make  very  nice  observations. 


Of  the  Solar  System.  51 

three  fourth  parts  of  the  surface  our  Earth  between 
the  polar  circles  are  covered  with  water,  and  that  lit- 
tle more  than  one  fourth  is  dry  land.  The  doctor 
omitted  weighing  all  within  the  polar  circles ;  be- 
cause there  is  no  certain  measurement  of  the  land 
within  them,  so  as  to  know  what  proportion  it  bears 
to  the  sea. 

52.  The  MOON  is  not  a  planet,  but  only  a  satel-The 
lite  or  attendant  of  the  Earth ;  going  round  the  Earth  M 
from  change  to  change  in  29  days  12  hours  and  44 
minutes ;  and  round  the  Sun  with  it  every  year.  The 
Moon's  diameter  is  2180  miles;  and  her  distance 
from  the  Earth's  centre  240  thousand.     She  goes 
round  her  orbit  in  27  days  7  hours  43  minutes, 
moving  about  2290  miles  every  hour;  and  turns 
round  her  axis  exactly  in  the  time  that  she  goes  round 
the  Earth,  which  is  the  reason  of  her  keeping  always 
the  same  side  toward  us,  and  that  her  day  and  night, 
taken  together,  is  as  long  as  our  lunar  month. 

53.  The  Moon  is  an  opaque  globe,  like  the  Earth,  Her 
and  shines  only  by  reflecting  the  light  of  the  Sun  :  Phase 
therefore,  while  that  half  of  her  which  is  toward  the 
Sun  is  enlightened,  the  other  half  must  be  dark  and 
invisible.     Hence,  she  disappears  when  she  comes 
between  us  and  the  Sun  ;  because  her  dark  side  is 
then  toward  us.     When  she  is  gone  a  little  way 
forward,  we  see  a  little  of  her  enlightened  side ; 
which  still  increases  to  our  view,  as  she  advances 
forward,  until  she  comes  to  be  opposite  to  the  Sun ; 

and  then  her  whole  enlightened  side  is  toward  the 
Earth,  and  she  appears  with  a  round  illumined  orb, 
which  we  call  the^//  moon :  her  dark  side  being 
then  turned  away  from  the  Earth.  From  the  full 
she  seems  to  decrease  gradually  as  she  goes  through 
the  other  half  of  her  course ;  shewing  us  less  and 
less  of  her  enlightened  side  every  day,  till  her  next 
change  or  conjunction  with  the  Sun,  and  then  she 
disappears  as  before. 


52  Of  the  Solar  System. 

A -proof  54.  This  continual  change  of  the  Moon's  phases 
'^es^wt  demonstrates  that  she  shines  not  by  any  light  of  her 
•by  her  own ;  for  if  she  did,  being  globular,  we  should  ai- 
ovm  light.  Ways  see  her  with  a  round  full  orb  like  the  Sun. 

Her  orbit  is  represented  in  the  scheme  by  the  little 
*J£-L      circles,  upon  the  Earth's  orbit  ®.     It  is  indeed 

drawn  fifty  times  too  large   in  proportion    to  the 

Earth's;  and  yet  is  almost  to  small  too  be  seen  in  the 

diagram. 
One  hair       55^  The  Moon  has  scarce  any  difference  of  sea- 

of  her  al-  ,  .     .  J  ,. 

•ways en-  sons;  her  axis  being  almost  perpendicular  to  the 
lightened,  ecliptic.  What  is  very  singular,  one  half  of  her 
has  no  darkness  at  all ;  the  Earth  constantly  afford- 
ing it  a  strong  light  in  the  Sun's  absence ;  while 
the  other  half  has  a  fortnight's  darkness,  and  a  fort- 
night's light  by  turns. 

Our  Earth  56.  Our  Earth  is  a  moon  to  the  Moon;  waxing 
Tnooo,  ar*d  waneing  regularly,  but  appearing  thirteen  times 
as  big,  and  affording  her  thirteen  times  as  much 
light,  as  she  does  to  us.  When  she  changes  to  us, 
the  Earth  appears  full  to  her ;  and  when  she  is  in 
her  first  quarter  to  us,  the  Earth  is  in  its  third  quar- 
ter to  her ;  and  vice  versa. 

57.  But  from  one  half  of  the  Moon,  the  Earth 
is  never  seen  at  all.     From  the  middle  of  the  other 
half,  it  is  always  seen  over  head ;  turning  round  al- 
most thirty  times  as  quick  as  the  Moon  does.  From 
die  circle  which  limits  our  view  of  the  Moon,  only 
one  half  of  the  Earth's  side  next  her  is  seen ;  the 
other  half  being  hid  below  the  horizon  of  all  places 
on  that  circle.     To  her,  the  Earth  seems  to  be  the 
largest  body   in  the  universe :  appearing  thirteen 
times  as  large  as  she  does  to  us. 

58.  The  Moon  has  no  atmosphere  of  any  visi- 
ble density  surrounding  her,  as  we  have  :  for  if  she 
had,  we  could  never  see  her  edge  so  well  defined 

A  proof  as  it  appears ;  but  there  would  be  a  sort  of  mist 
Moon's  or  haz*ness  around  her,  which  would  make  the 
having  no  stars  look  fainter,  when  they  are  seen  through  it. 


atmos-      But  observation  proves,  that  the  stars  which  disap- 


Of  the  Solar  System. 

pear  behind  the  Moon,  retain  their  full  lustre  until 
they  seem  to  touch  her  very  edge,  and  then  they 
vanish  in  a  moment.  This  has  been  often  observed 
by  astronomers,  but  particularly  byCAssiNi  of  the 
star  «p  in  the  breast  of  Virgo,  which  appears  single 
and  round  to  the  bare  eye  j  but  through  a  refracting 
telescope  of  16  feet,  appears  to  be  two  stars  so  near 
together,  that  the  distance  between  them  seems  to 
be  but  equal  to  one  of  their  apparent  diameters. 
The  moon  was  observed  to  pass  over  them  on  the 
21st  of  April  1720,.  A*.  S.  and  as  her  dark  edge 
drew  near  to  them,  it  caused  no  change  whatever 
in  their  colour  or  situation.  At  25  min.  14  sec. 
past  12  at  night,  the  most  westerly  of  these  stars  was. 
hid  by  the  dark  edge  of  the  Moon ;  and  in  30  se- 
conds afterward,  the  most  easterly  star  was  hid :  each 
of  them  disappearing  behind  the  Moon  in  an  instant, 
without  any  preceding  diminution  of  magnitude  or 
brightness ;  \vhich  by  no  means  could  have  been  the 
case  if  there  were  an  atmosphere  round  the  Moon  : 
for  then  one  of  the  stars  falling  obliquely  into  it  be- 
fore the  other,  ought,  by  refraction,  to  have  suffered 
some  change  in  its  colour,  or  in  its  distance  from  the 
other  star,  which  was  not  yet  entered  into  the  atmos- 
phere. But  no  such  alteration  could  be  perceived ; 
though  the  observation  was  made  with  the  utmost 
attention  to  that  particular ;  and  was  very  proper  to 
have  made  such  a  discovery.  The  faint  light  which 
has  been  seen  all  round  the  Moon,  in  total  eclipses 
of  the  Sun,  has  been  observed,  during  the  time  of 
darkness,  to  have  its  centre  coincident  with  the  cen- 
tre of  the  Sun  ;  and  was  therefore  much  more  likely 
to  arise  from  the  atmosphere  of  the  Sun,  than  from 
that  of  the  Moon ;  for  if  it  had  been  owing  to  the 
latter,  its  centre  would  have  gone  along  with  the 
Moon's.* 

*  It  has  been  lately  ascertained  by  Mr.  Schroeter,  that  the  Moon 
is  indeed  furnished  with  an  atmosphere,  similar  to  that  cf  the  Earth, 
and  of  proportional  density ;  the  former  being  about  one  29th  par? 
the  density  of  the  latter. 


54  Of  the  Solar  System 

Nor  seas,  5 9<  jf  tnere  were  seas  jn  the  Moon,  she  could  have 
no  clouds,  rains,  or  storms,  as  we  have ;  because 
she  has  no  such  atmosphere  to  support  the  vapours 
which  occasion  them.  And  every  one  knows,  that 
when  the  Moon  is  above  our  horizon  in  the  night 
time,  she  is  visible,  unless  the  clouds  of  our  atmos- 
phere hide  her  from  our  view;  and  all  parts  of  her 
appear  constantly  with  the  same  clear,  serene,  and 

of  c^erns  CallT1  aSPCCt-       But   th°SC    dark    PartS    of  the  Moon, 

and  deep  which  were  formerly  thought  to  be  seas,  are  now 
pits.         found  to  be  only  vast  deep  cavities,  and  places  which 
reflect  not  the  Sun's  light  so  strongly  as  others ;  hav- 
ing many  caverns  and  pits,  whose  shadows  fall  with- 
in them,  and  are  always  dark  on  the  side  next  the 
Sun.     This  demonstrates  their  being  hollow  :  and 
most  of  these  pits  have  little  knobs  like  hillocks 
standing  within  them,  and  casting  shadows  also ; 
which  cause  these  places  to  appear  darker  than  others 
which  have  fewer,  or  less  remarkable  caverns.     All 
these  appearances  shew  that  there  are  no  seas  in  the 
Moon  ;  for  if  there  were  any,  their  surfaces  \vould 
appear  smooth  and  even  like  those  on  the  Earth. 
The  stars      60.  There  being  no  atmosphere  about  the  Moon, 
s!bieytoVI"tne  heavens  in  the  day  time  have  the  appearance  of 
the  Moon,  night  to  a  Lunarian  who  turns  his  back  toward  the 
Sun ;  the  stars  then  appearing  as  bright  to  him  as 
they  do  in  the  night  to  us.     For  it  is  entirely  owing 
to  our  atmosphere  that  the  heavens  are  bright  about 
us  in  the  day. 

61.  As  the  Earth  turns  round  its  axis,  the  several 
continents,  seas,  and  islands,  appear  to  the  Moon's 
inhabitants  like  so  many  spots  of  different  forms  and 
brightness,  moving  over  its  surface ;  but  much  faint- 
er at  some  times  than  others,  as  our  clouds  cover 
The  Earth  them  or  leave  them.     By  these  spots  the  Lunarians 
the  Moon. can  determine  the  time  of  the  Earth's  diurnal  motion, 
just  as  we  do  the  motion  of  the  Sun  ;  and  perhaps 
they  measure  their  time  by  the  motion  of  the  Earth's 
spots;  for  they  cannot  have  a  truer  dial, 


Of  the  Solar  System.  55 

62.  The  Moon's  axis  is  so  nearly  perpendicular  Plate  /. 
to  the  ecliptic,  that  the  Sun  never  removes  sensibly 
from  her  equator  :  and  the  *  obliquity  of  her  orbit, 
which  is  next  to  nothing  as  seen  from  the  Sun,  can- 
not cause  the  Sun  to  decline  sensibly  from  her  equa- 
tor.    Yet  her  inhabitants  are  not  destitute  of  means  HOW  the 
for  ascertaining  the  length  of  their  year,  though  their 


method  and  ours  must  differ.  We  can  know  the  the  length 
length  of  our  year  by  the  return  of  our  equinoxes  ;  }° 
but  the  Lunarians,  having  always  equal  day  and 
night,  must  have  recourse  to  another  method  ;  and 
we  may  suppose,  they  measure  their  year  by  observ- 
ing when  either  of  the  poles  of  our  Earth  begins  to 
be  enlightened,  and  the  other  to  disappear,  which  is 
always  at  our  equinoxes;  they  being  conveniently 
situate  for  observing  great  tracts  of  land  about  our 
Earth's  poles,  which  are  entirely  unknown  to  us. 
Hence  we  may  conclude,  that  the  year  is  of  the 
same  absolute  length  both  to  the  Earth  and  Moon, 
though  very  different  as  to  the  number  of  days  :  we 
having  365-J  natural  days,  and  the  Lunarians  only 
12—  ;  every  day  and  night  in  die  Moon  being  as 
as  long  as  29j  on  the  Earth* 

63.  The  Moon's  inhabitants,  on  the  side  next  the  and  the 
Earth,  may  a§  easily  find  the  longitude  of  their  pla-^fheh- 
ces  as  we  can  find  the  latitude  of  ours.     For  the  places. 
Earth  keeping  constantly,  or  very  nearly  so,  over 

one  meridian  of  the  Moon,  the  east  or  west  distan- 
ces of  places  from  that  meridian  are  as  easily  found, 
as  we  can  find  our  distance  from  the  equator  by  the 
altitude  of  our  celestial  poles. 

64.  The  planet  MARS  is  next  in  order,  being  the  Mars, 
first  above  the  Earth's  orbit.     His  distance  from  the 
Sun  is  computed  to  be  125  millions  of  miles  ;  and 

*  The  Moon's  orbit  crosses  the  ecliptic  in  two  opposite  points, 
called  the  moon's  nodes;  so  that  one  half  of  her  orbit  is  above  the 
ecliptic,  and  the  other  half  below  it.  The  angle  of  its  obliquity  is 
5  1-3  degrees. 

H 


56  Of  the  Solar  System. 

by  travelling  at  the  rate  of  47  thousand  miles  every 
$S>  *••     hour,  in  the  circle  <p  ,  he  goes  round  the  Sun  in  686 
of  our  days  and  23  hours,  which  is  the  length  of  his 
year,  and  contains  66 7~  of  his  days ;  every  day  and 
night  together  being  40  minutes  longer  than  with  us. 
His  diameter  is  4444  miles ;  and  by  his  diurnal  ro- 
tation, the  inhabitants  about  his  equator  are  carried 
556  miles  every  hour.     His  quantity  of  light  and 
heat  is  equal  but  to  one  half  of  ours ;  and  the  Sun 
appears  but  half  as  large  to  his  inhabitants  as  to  us. 
His  at-          65.  This  planet  being  but  a  fifth  part  of  the  mag- 
mosphere  nitude  of  the  Earth,    if  any  moon  attends  him,  it 
and  phas-  must  j^e  verv  sm^  an(j  ]ias  not  yet  been  discover. 

ed  by  our  best  telescopes.  He  is  of  a  fiery  red  co- 
lour, and  by  his  appulses  to  some  of  the  fixed  stars, 
seems  to  be  encompassed  by  a  very  gross  atmos- 
phere. He  appears  sometimes  gibbous,  but  never 
horned;  which  shews  both  that  his  orbit  includes  the 
Earth's  within  it,  and  that  he  shines  not  by  his  own 
light. 

66.  To  Mars,  our  Earth  and  Moon  appear  like 
two  moons,  a  larger  and  a  less :  changing  places 
with  one  another,  and  appearing  sometimes  horned, 
sometimes  half  or  three  quarters  illuminated,  but 
never  full ;  nor  at  most  above  one  quarter  of  a  de- 
gree from  each  other ;  although  they  are  240  thou- 
sand miles  asunder. 

HOW  the       67.  Our  Earth  appears  almost  as  large  to  Mars  aa 
other  pia-  Venus  does  to  us  ;  and  at  Mars  it  is  never  seen  above 
pear  to"    4^  degrees  from  the  Sun.  Sometimes  it  appears  to 
Mars,       pass  over  the  disc  of  the  Sun,  and  so  do  Mercury 
and  Venus.    But  Mercury  can  never  be  seen  from 
Mars  by  such  eyes  as  ours,  unassisted  by  proper  in- 
struments; and  Venus  will  be  as  seldom  seen  as  we 
see  Mercury.    Jupiter  and  Saturn  are  as  visible  to. 
the  inhabitants  of  Mars  as  to  us.     His  axis  is  per, 
'  pendicular  to  the  ecliptic,  and  his  orbit  is  inclined  to 

it  in  an  angle  of  1  degree  50  minutes. 
Jupiter.        68'  JUPITER>  tne  largest  of „ all  the  planets,  ia 
still  higher  in  the  system,  being  about  426  millions. 


Of  the  Solar  System.  57 

of  miles  from  the  Sun :  and  going  at  the  rate  of ^f.ate  L 
25  thousand  miles  every  hour,  in  his  orbit,  which 
is  represented  by  the  circle  % .  He  finishes  his  an- 
nual period  in  eleven  of  our  years  314  days  and  12 
hours.  He  is  above  1000  times  as  large  as  the 
Earth;  his  diameter  being  81,000  miles;  which 
is  more  than  ten  times  the  diameter  of  the  Earth. 

69.  Jupiter  turns  round  his  axis  in  9  hours  56  the  num. 
minutes;    so  that  his  year  contains    10  thousand ^Pj^f 

1  1  •  i*  r*        t     •  •  HAS    »  C<**  » 

470  days ;  the  diurnal  velocity  of  his  equatorial 
parts  being  greater  than  that  with  which  he  moves 
in  his  annual  orbit — a  singular  circumstance,  as 
far  as  we  know.  By  this  prodigious  quick  rota- 
tion, his  equatorial  inhabitants  are  carried  25  thou- 
sand 920  miles  every  hour  (which  is  920  miles  an 
hour  more  than  an  inhabitant  of  our  Earth's  equa- 
tor moves  in  24  hours)  beside  the  25  thousand 
above  mentioned,  which  is  common  to  all  parts  of 
his  surface,  by  his  annual  motion. 

70.  Jupiter  is  surrounded  by  faint  substances,  His  belts 
called  belts;  in  which  so  many  changes  appear, an 
that  they  are  generally  thought  to  be  clouds;  for 
some  of  them  have  been  first  interrupted  and  bro- 
ken, and  then  have  vanished  entirely.     They  have 
sometimes  been  observed  of  different  breadths,  and 
afterward   have   all  become   nearly   of   the   same 
breadth.  Large  spots  have  been  seen  in  these  belts ; 

and  when  a  belt  vanishes,  the  contiguous  spots  dis- 
appear with  it.  The  broken  ends  of  some  belts 
have  been  generally  observed  to  revolve  in  the  same 
time  with  the  spots :  only  those  nearer  the  equator 
in  somewhat  less  time  than  those  near  the  poles ; 
perhaps  on  account  of  the  Sun's  greater  heat  near 
the  equator,  which  is  parallel  to  the  belts  and  course 
of  the  spots.  Several  large  spots,  which  appear 
round  at  one  time,  grow  oblong  by  degrees,  and 
then  divide  into  two  or  three  round  spots.  The 
periodical  time  of  the  spots  near  the  equator  is  9 
hours  50  minutes, v  but  of  these  near  the  poles  9 
hours  56  minutes.  See  Dr.  SMITH'S  Optics, 
5  1004,  &  sej. 


58  Of  the  Solar  System. 


of  ^**  ^e  ax*s  °^  Jupiter  'ls  so  nearly  perpendicu- 
;  lar  to  his  orbit,  that  he  has  no  sensible  change  of 
seasons;  which  is  a  great  advantage,  and  wisely 
ordered  by  the  Author  of  Nature.  For,  if  the 
axis  of  this  planet  were  inclined  any  considerable 
number  of  degrees,  just  so  many  degrees  round 
each  pole  would  in  their  turn  be  almost  six  of  our 
years  together  in  darkness.  And,  as  each  degree 
of  a  great  circle  on  Jupiter  contains  706  of  our 
miles,  at  a  mean  rate,  it  is  easy  to  judge  what  vast 
tracts  of  land  would  be  rendered  uninhabitable  by 
any  considerable  inclination  of  his  axis. 
but  has  72.  The  Sun  appears  but  ~  part  as  large  to  Ju- 

Soons  P*ter  as  to  us  ;  anc*  kis  light  and  heat  are  in  the 
same  small  proportion,  but  compensated  by  the 
quick  returns  thereof,  and  by  four  moons  (some 
larger  and  some  less  than  our  Earth)  which  revolve 
about  him  :  so  that  there  is  scarce  any  part  of  this 
huge  planet,  but  what  is,  during  the  whole  night, 
enlightened  by  one  or  more  of  these  moons  ;  except 
his  poles,  where  only  the  farthest  moons  can  be 
seen,  and  where  light  is  not  wanted  ;  because  the 
Sun  constantly  circulates  in  or  near  the  horizon, 
and  is  very  probably  kept  in  view  of  both  poles  by 
the  refraction  of  Jupiter's  atmosphere,  which,  if  it 
be  like  ours,  has  certainly  refractive  power  enough 
for  that  purpose. 

Their  pe-      73.  The  orbits  of  these  moons  are  represented  in 
nods        tke  scnerne  Of  the  solar  system  by  four  small  circles 

round  Ju-          *•»'«••,-*..«  T      •  i  • 

piter.  *  marked  1,2,  3,  4,  on  Jupiter's  orbit  2/  ;  drawn,  in- 
deed,  fifty  times  too  large  in  proportion  to  it. 
The  first  moon,  or  that  nearest  to  Jupiter,  goes 
round  him  in  1  day  18  hours  and  36  minutes  of  our 
time  ;  and  is  229  thousand  miles  distant  from  his 
centre:  the  second  performs  its  revolution  in  3  days 
13  hours  and  15  minutes,  at  364  thousand  miles  dis- 
tance: the  third  in  7  days  3  hours  and  59  minutes, 
at  the  distance  of  580  thousand  miles  :  and  the  fourth, 
or  outermost,  in  16  days  18  hours  and  30  minutes, 
at  the  distance  of  one  million  of  miles  from  his  centre., 


Of  the  Solar  Sys' 


cm. 


74.  The  angles  under  which  the  orbits  of  Jupi- 

,,  i       T-       i  •  of  their  or- 

ter's  moons  are  seen  from  the  iLarth,  at  its  mean  bits,  and 
distance  from  Jupiter,  are  as  follows  :     The  first,  distances 
3'  55";  the  second,  6'  14";  the  third,  9'  58";  and  {£m  Jui 
the  fourth,  17'  30".     And  their  distances  from  Ju- 
piter, measured  by  his  semi-diameters,  are  thus  : 
The  first,  5f;  the  second  9,  the  third,  14|J;  and 
the  fourth,    25~*.       This  planet,  seen  from  its  HOW  he 
nearest  moon,  appears  1000  times  as  laree  as  our  aPPears  t& 

,.  ,  .  -  11  i        his  nearest 

Moon  does  to  us;  waxing  and  waneing  in  all  her  moon. 
monthly  shapes,  every  42-  hours. 

75.  Jupiter's   three  nearest  moons  fall  into  his  Two 
shadow,  and  are  eclipsed  in  every  revolution  :  butteries'55" 
the  orbit  of  the  fourth  moon  is  so  much  inclined,  made  by 
that  it  passes  by  its  opposition  to  Jupiter,  without  e^of  jupi- 
falling  into  his  shadow,  two  years  in  every  six.  Byter's 
these  eclipses,  astronomers  have  not  only  discov-  moons- 
cred  that  the  Sun's  light  takes  up  eight  minutes  of 

time  in  coming  to  us  ;  but  they  have  also  determin- 
ed the  longitudes  of  places  on  this  Earth,  with 
greater  certainty  and  facility,  than  by  any  other  me- 
thod yet  known  ;  as  shall  be  explained  in  the  ele- 
venth chapter. 

76.  The  difference  between  the  equatorial  and  J.1^  £reat 
polar  diameters  of  Jupiter  is  6230  miles  ;  for  his  better 
equatorial  diameter  is  to  his  polar,  as  13  to  12.   Sothe.e(iua- 
that  his  poles  are  3115  miles  nearer  his  centre  than  anTpoiar 
his  equator  is.     This  results  from  his  quick  motion  diameters 
round  his  axis;  for  the  fluids,  together  with  theot  Juplter' 
light  particles,  which  they  can  carry  or  wash  away 

with  them,  recede  from  the  poles,  which  are  at 
rest,  toward  the  equator,  where  the  motion  is 
quickest;  until  there  be  a  sufficient  number  accu- 
mulated to  make  up  the  deficiency  of  gravity  lost 
by  ^  the  centrifugal  force  which  always  arises  from  a 
quick  motion  round  an  axis  :  and  when  the  defi- 
ciency of  wdght  or  gravity  of  the  particles  is  made 
up  by  a  sufficient  accumulation,  there  is  an  equili- 

*    CASSINI  JSlemens  d'SlstronQinie,  Liv.  ix.  Chafi,   3, 


60  Of  the  Solar  System. 

Plate  I.     brium,  and  the  equatorial  parts  rise  no  higher.    Our 
The  dif-    Earth  being  but  a  very  small  planet,  compared  with 
[ut!"^n     ^piter,  and  its  motion  round  its  axis  being  much 
those  of    slower,  it  is  less  flattened  of  course.     The  propor- 
our  Earth,  tion  between  its  equatorial  and  polar  diameters  be- 
ing only  as  230  to  229  ;  and  their  difference   36 
miles.* 

Place  of        77.  Jupiter's  orbit  is  inclined  to  the  ecliptic  in  an 
his  nodes.  angle  of  !  degree  20  minutes.    His  ascending  node 
is  in  the  8th  degree  of  Cancer,  and  his  descending 
node  in  the  8th  degree  of  Capricorn. 

Saturn.  78.  SATURN,  the  remotest  of  all  the  planets,f 
is  about  780  millions  of  miles  from  the  Sun  ;  and 
travelling  at  the  rate  of  18  thousand  miles  every 
Fig.  I.  hour,  in  the  circle  marked  ^  >  performs  its  annual 
circuit  in  29  years  167  days,  and  5  hours  of  our 
time ;  which  makes  only  one  year  to  that  planet. 
Its  diameter  is  67,000  miles;  and  therefore  it  is 
near  600  times  as  large  as  the  Earth. 
His  ring-.  79.  This  planet  is  surrounded  by  a  thin  broad 
Fi§r-  v-  ring,  as  an  artificial  globe  is  by  an  horizon.  The 
ring  appears  double  when  seen  through  a  good  tele- 
scope, and  is  represented,  by  the  figure,  in  such  an 
oblique  view  as  that  in  which  it  generally  appears. 
It  is  inclined  30  degrees  to  the  ecliptic,  and  is 
about  21  thousand  miles  in  breadth;  which  is  equal 
to  its  distance  from  Saturn  on  all  sides.  There  is 
reason  to  believe  that  the  ring  turns  round  its  axis ; 

*  According  to  the  French  measures,  a  degree  of  the  meridian  at 
the  equator  contains  340606.63  French  feet ;  and  a  degree  of  the 
meridian  in  Lapland  contains  344627. 40 :  so  that  a  degree  in  Lap- 
land is  4020.72  French  feet  (or  4280.02  English  feet)  longer  than  a 
degree  at  the  equator.  The  difference  is  J^  parts  of  an  English 
mile.— Hence,  the  Earth's  equatorial  diameter  contains  39386196 
French  feet,  or  41926356  English  ;  and  the  polar  diameter  3y202920 
French  feet,  or  41731272  English.  The  equatorial  diameter  there- 
fore is  195084  English  feet,  or  36.948  English  miles,  longer  than  the 
axis, 
t  The  Georgian  planet  was  not  discovered  when  this  was  written* 


Of  the  Solar  System.  61 

because,  when  it  is  almost  edge- wise  to  us,  it  ap- Platc  L 
pears  somewhat  thicker  on  one  side  of  the  planet 
than  on  the  other  ;  and  the  thickest  edge  has  been 
seen  on  different  sides  at  different  times*.  Saturn 
having  no  visible  spots  on  his  body,  whereby  to  de- 
termine the  time  of  his  turning  round  his  axis, 
the  length  of  his  days  and  nights,  and  the  position 
of  his  axis,  are  unknown  to  usf. 

80.  To  Saturn,  the  Sun  appears  only  ~th  part  as  His  five 
large  as  to  us ;  and  the  light  and  heat  he  receives  moons. 
from  the  Sun  are  in  the  same  proportion  to  ours. 
But  to  compensate  for  the  small  quantity  of  sun- 
light, he  has  five  moons,  all  going  round  him  on  the 
out- side  of  his  ring,  and  nearly  in  the  same  plane 
with  it.  The  first,  or  nearest  moon  to  Saturn,  goes 
round  him  in  1  day  21  hours  19  minutes;  and  is 
140  thousand  miles  from  his  centre  :  the  second,  in 
2  days  17  hours  40  minutes;  at  the  distance  of  187 
thousand  miles  .  the  third,  in  4  days  12  hours  25 
minutes ;  at  263  thousand  miles  distance :  the  fourth, 
in  15  days  22  hours  41  minutes;  at  the  distance  of 
600  thousand  miles :  and  the  fifth,  or  outermost,  at 
one  million  800  thousand  miles  from  Saturn's  cen- 
tre, goes  round  him  in  79  days  7  hours  48  min- 
utes J.  Their  orbits,  in  the  scheme  of  the  solar  sys-  Fig.  i. 


*  Dr.  Herschel,  from  some  srxrts  he  has  seen  on  the  exterior  ring, 
has  determined  that  it  revolves  in  about  10  1-2  hours. 

t  Dr.  Herschel  having  discovered  that  there  are  some  belt-like 
appearances  on  this  planet,  similar  to  those  which  are  seen  on  Jupi- 
ter, concluded  that  it  must  revolve  on  its  axis,  and  that  with  a  pretty 
quick  motion.  He  also  thinks  he  has  determined,  from  some  parts  of 
those  belts  which  are  less  black  than  others,  that  this  revolution  is 
performed  in  10  hours  16  minutes. 

\  Dr.  Herschel  has  discovered  two  other  moons  belonging  to  Sa- 
turn, which  revolves  between  the  nearest  of  the  old  ones  and  the  pla- 
net ;  so  that  Saturn  is  now  known  to  have  seven  moons.  The  exteri- 
or of  the  new  satellites,  called  the  sixth,  revolves  at  the  distance  ot 
near  120  thousand  miles,  in  one  day  8  hours  53  minutes;  and  that 
which  is  nearest  the  primary,  termed  the  seventh,  is  distant  from  it 
about  91  thousand  miles,  and  performs  its  revolution  in  22  hours  37 
minutes:  but  the  Doctor  esteems  this  last  article  rather  uncertain. 
Jie  has  moreover  discovered  that  the  fifth  satellite  revolves  on  its 


Of  the  Solar  System. 

tern,  are  represented  by  the  five  small  circles,  mark. 
ed  1,  2,  3,  4,  5,  on  Saturn's  orbit;  but  these,  like 
the  orbits  of  the  other  satellites,  are  drawn  fifty  times 
too  large  in  proportion  to  the  orbits  of  their  primary 
planets. 

81.  The  Sun  shines  almost  fifteen  of  our  years 
together  on  one  side  of  Saturn's  ring  without  set- 
ting, and  as  long  on  the  other,  in  its  turn.  So  that 
the  ring  is  visible  to  the  inhabitants  of  that  planet 
for  almost  fifteen  of  our  years,  and  as  long  invisible, 
by  turns,  if  its  axis  have  no  inclination  to  its  ring  : 
but  if  the  axis  of  the  planet  be  inclined  to  the  ring, 
suppose  about  30  degrees,  the  ring  will  appear  and 

his  ring,  disappear  once  every  natural  day,  to  all  the  inhabi- 
tants within  30  degrees  of  the  equator  on  both 
sides,  frequently  eclipsing  the  Sun  in  a  Saturnian 
day.  Moreover,  if  Saturn's  axis  be  thus  inclined 
to  his  ring,  it  is  perpendicular  to  his  orbit;  and 
thereby  the  inconvenience  of  different  seasons  to 
that  planet  is  avoided.  For  considering  the  length 
of  Saturn's  year,  which  is  almost  equal  to  30  of 
ours,  what  a  dreadful  condition  must  the  inhabitants 
of  his  polar  regions  be  in,  if  they  be  half  that  time  de- 
prived of  the  light  and  heat  of  the  Sun!  which  is  not 
their  case  alone,  if  the  axis  of  the  planet  be  perpendi- 
cular to  the  ring,  for  then  the  ring  must  hide  the  Sun 
from  vast  tracts  of  land  on  each  side  of  the  equator 
for  13  or  14  of  our  years  together,  on  the  south  side 
and  north  side,  by  turns,  as  the  axis  inclines  to  or 
from  the  Sun.  This  furnishes  another  good  pre- 
sumptive proof  of  the  inclination  of  Saturn's  axis 
to  its  ring,  and  also  of  his  axis  being  perpendicular 
to  its  orbit. 

HOW  the       82.    This  ring,   seen  from  Saturn,  appears  like 
a  vast  luminous  arch  in  the  heavens,   as  if  it  did 


Saturn 

and  to  us. 

axis,  as  our  Moon  does,  in  the  same  time  it  revolves  in  its  orbit  :  a 
very  remarkable  as  well  as  curious  coincidence  in  the  motions  of  the 
secondaries  to  two  different,  and  very  distant  primaries.  And  it  is 
probably  a  general  law  of  nature,  that  all  secondary  planets  con- 
stantly present  the  same  face  towards  \heirfirimaries. 


Of  the  Solar  System.  63 

not  belong  to  the  planet.      When  we  see  the   ring 
most  open,  its  shadow  upon  the  planet  is  broadest; 
and  from  that  time  the  shadow  grows  narrower,  as 
the  ring  appears  to  do  to  us  ;   until  by  Saturn's  an- 
nual motion  the  Sun  comes  to  the  plane  of  the  ring, 
or  even  with  its  edge ;  which  being  then  directed  to- 
ward us,  becomes  invisible  on  account  of  its  thin- 
ness ;  as  shall  be  explained  more  largely  in  the  tenth 
chapter,  and  illustrated  by  a  figure.     The  ring  dis-  in  what 
appears  twice  in  every  annual  revolution  of  Saturn ;  ^iTap** 
namely,  when  he  is  in  the  -20th  degrees  of  Pisces  and  pears  to 
of  Virgo.     And  when  Saturn  is  in  the  middle  be-^f^ 
tween  these  points,  or  in  the  20th  degree  either  of  in  what 
Gemini  or  of  Sagittarius,  hi&ring  appears  most  open  *ign^s 
to  us;  and  then  its  longest  diameter  is  to  its  shortest,  S£>st  open 
as  9  to  4.  tous- 

83.  To  such  eyes  as  ours,  unassisted  by  instru- _ 

T       .         .  J    ,  J .  No  planet 

ments,  Jupiter  is  the  only  planet  that  can  be  seen  but  Sa-  ' 
from  Saturn  ;  and  Saturn  the  only  planet  that  can  be  turn  can  be 
seen  from  Jupiter.     So  that  the  inhabitants  of  these  jupherT 
two  planets  must  either  see  much  farther  than  we  do,  nor  any ' 
or  have  equally  good  instruments  to  carry  their  sight  [™™b^" 
to  remote  objects,  if  they  know  that  there  is  such  a  sides  ju- 
body  as  our  Earth  in  the  universe;  for  the  Earth  isPiter- 
no  larger,  seen  from  Jupiter,  than  his  moons  are,  seen 
from  the  Earth;  and  if  his  large  body  had  not  first 
attracted  our  sight,  and  prompted  our  curiosity  to 
view  him  with  a  telescope,   we  should  never  have 
known  any  thing  of  his  moons;   unless  indeed  by  I 

chance,  we  had  directed  the  telescope  toward  that 
small  part  of  the  heavens  where  they  were,  at  the  time 
of  observation.  And  the  like  is  true  of  the  moons  of 
Saturn. 

84.  The  orbit  of  Saturn  is  2i  degrees  inclined  to  puce  qf 
the  ecliptic  or  orbit  of  our  Earth,  and  intersects  it 

in  the  22d  degrees  of  Cancer  and  of  Capricorn  ;  so 
that  Saturn's  nodes  are  only  14  degrees  from  those 
of  Jupiter,  §  77*. 

*  Since  Mr.  Ferguson's  death,  a  seventh  primary  planet,  belong-  G 
ing  to  the  solar  system,  has  been  discovered  by  Dr,  Herschel,  and  Si 


64  Of  the  Solar  System. 


35.  The  quantlty  of  light  afforded  by  the  Sun  to 
much  Jupiter,  being  but  Ath  part,  and  to  Saturn  only  -sVh 
stronger^  part  of  what  we  enjoy  ;  may  at  first  thought  induce  us 
and  Sa-  **  to  believe  that  these  two  planets  are  entirely  unfit  for 
turn  than  rational  beings  to  dwell  upon.  But,  that  their  light 
ly  behey1.  "  *s  not  so  we^k  as  we  imagine,  is  evident  from  their 
ed.  brightness  in  the  night-time  ;  and  also  from  this  re- 
markable phenomenon,  —  that  when  the  Sun  is  so 

called  by  him,  the  Georgium  Sidus,  out  of  respect  to  his  pre- 
sent Majesty  King  George  the  III.  This  planet  is  still  higher  in  the 
system  than  Saturn,  being  about  1565  millions  of  miles  from  the 
Sun  ;  and  performs  its  annual  circuit  in  83  years,  140  days  and  8 
hours  of  our  time:  consequently  its  motion  in  its  orbit,  is  at  the  rate 
of  about  7  thousand  miles  in  an  hour.  To  a  good  eye  unassisted 
by  a  telescope,  this  planet  appears  like  a  faint  star  of  the  5th  mag- 
nitude ;  and  cannot  be  readily  distinguished  from  a  fixed  star  with 
a  less  magnifying  power  than  200  times.  Its  apparent  diameter 
subtends  an  angle  of  no  more  than  4"  to  an  observer  on  the  Earth  ; 
but  its  real  diameter  is  about  34,000  miles,  and  consequently,  it  is 
about  80  times  as  large  as  the  Earth.  Hence  we  may  infer  that  as 
the  Earth  cannot  be  seen  under  an  angle  of  quite  1"  to  the  inhabi- 
tants of  the  Georgian  planet,  it  has  never  yet  been  seen  by  them, 
unless  their  eyes  and  instruments  are  considerably  better  than  ours. 
The  orbit  of  this  planet  is  inclined  to  the  ecliptic  in  an  angle  of 
46'  26".  Its  ascending  node  is  in  the  13th  degree  of  Gemini,  and 
its  descending  node  in  the  13th  degree  of  Sagittarius.  As  no  spots 
have  yet  been  discovered  on  its  surface,  the  position  of  its  axis,  and 
the  length  of  its  day  and  night  are  not  known. 

On  account  of  the  immense  distance  of  the  Georgian  planet  from 
the  source  of  light  and  heat  to  all  the  bodies  in  our  system,  it  was 
highly  probable  that  several  satellites,  or  moons  revolved  round  it  : 
accordingly,  the  high  powers  of  Dr.  Herschel's  telescopes  have  en- 
abled him  to  discover  six  ;  and  there  may  be  others  which  he  has 
not  yet  seen.  The  first,  and  nearest  to  the  planet,  revolves  at  the 
distance  of  12  of  the  planet's  semi-diameters  from  it,  and  performs 
its  revolution  in  5  days,  21  hours  25  minutes  :  the  second  i  evolves 
at  16  1-2  semi-diameters  of  the  primary  from  it,  and  completes  its 
revolution  in  8  days  17  hours  1  minute  :  the  third  at  19  semi-diam- 
eters, in  10  clays  23  hours  4  minutes  :  the  fourth  at  22  semi-dia- 
meters, in  13  days  11  hours  5  minutes:  the  5th  at  44  semi-diame- 
ters, in  38  days  1  hour  49  minutes:  and  the  sixth  at  88  semi-dia- 
meters, in  107  days  16  hours  40  minutes.  It  is  remarkable  that  the 
orbits  of  these  Satellites  are  almost  at  right  angles  to  the  plane  of 
the  ecliptic:  and  that  the  motion  of  all  of  them,  in  their  orbits  is 
retrograde. 


Of  the  Solar  System.  65 

much  eclipsed  to  us,  as  to  have  only  the  40th  part 
of  his  disc  left  uncovered  by  the  Moon,  the  de- 
crease of  light  is  not  very  sensible ;  and  just  at  the 
end  of  darkness  in  total  eclipses,  when  his  western 
limb  begins  to  be  visible,  and  seems  no  bigger  than 
a  bit  of  fine  silver  wire,  every  one  is  surprised  at 
the  brightness  wherewith  that  small  part  of  him 
shines.  The  Moon,  when  full,  affords  travellers 
light  enough  to  keep  them  from  mistaking  their 
way;  and  yet,  according  to  Dr.  SMITH*,  it  is 
equal  to  no  more  than  a  90  thousandth  part  of  the 
light  of  the  Sun :  that  is,  the  Sun's  light  is  90  thou- 
sand times  as  strong  as  the  light  of  the  Moon  when 
full.  Consequently,  the  Sun  gives  a  thousand  times 
as  much  light  to  Saturn  as  the  full  Moon  does  to  us , 
and  above  three  thousand  times  as  much  to  Jupiter. 
So  that  these  two  planets,  even  without  any  moons, 
would  be  much  more  enlightened  than  we  at  first 
imagine ;  and  by  having  so  many,  they  may  be  ve- 
ry comfortable  places  of  residence.  Their  heat,  so 
far  as  it  depends  on  the  force  of  the  Sun's  rays,  is 
certainly  much  less  than  ours ;  to  which  no  doubt  the 
bodies  of  their  inhabitants  are  as  well  adapted  as  ours 
are  to  the  seasons  we  enjoy.  And  if  we  consider 
that  Jupiter  never  has  any  winter,  even  at  his  poles, 
which  probably  is  also  the  case  with  Saturn,  the 
cold  cannot  be  so  intense  on  these  two  planets  as  is 
generally  imagined.  Besides,  there  may  be  some- 
thing in  the  nature  of  their  soil,  that  renders  it  warm- 
er than  that  of  our  Earth ;  and  we  find  that  all  our  All  our 
heat  depends  not  on  the  rays  of  the  Sun  :  for  if  itp^d^ 
did,  we  should  always  have  the  same  months  equal-  on  the 
ly  hot  or  cold  at  their  annual  returns.  But  it  is 
otherwise,  for  February  is  sometimes  warmer  than 
May  ;  which  must  be  owing  to  vapours  and  exha- 
lations from  the  Earth. 

86.  Every  person  who  looks  upon,  and  compares 
the  systems  of  moons  together,  which  belong  to 

*  Optics,  Ajct  95. 


ravs. 


66  Of  the  Solar  System. 

Jupiter  and  Saturn  must  be  amazed  at  the  vast  mag- 
nitude of  these  two  planets,  and  the  noble  attend- 
ance they  have  in  comparison  with  our  little  Earth ; 
and  can  never  bring  himself  to  think,  that  an  infi- 
nitely wise  Creator  should  dispose  of  all  his  animals 
and  vegetables  here,  leaving  the  other  planets  bare 
it  is  high-  and   destitute  of  rational  creatures.      To  suppose 
WeUiaTail ^iat  ^e  ka(*  anv  v*cw  to  our  benefit,  in  creating  these 
the  plan-   moons,  and  giving  them  their  motions  round  Jupi- 
ter  and  Saturn;  to  imagine  that  he  intended  these 
vast  bodies  for  any  advantage  to  us,  when  he  well 
knew  they  could  never  be  seen  but  by  a  few  astrono- 
mers peeping  through  telescopes ;  and  that  he  gave 
to  the  planets  regular  returns  of  days  and  nights, 
and  different  seasons  to  all  where  they  would  be 
convenient;  but  of  no  manner  of  service  to  us;  ex- 
cept  only  what  immediately  regards  our  own  planet 
the  Earth.     To  imagine,  I  say,  that  he  did  all  this 
on  our  account,  would  be  charging  him,  impiouslyx 
with  having  done  much  in  vain ;  and  as  absurd  as 
to  imagine  that  he  has  created  a  little  sun  and  a  pla- 
netary system  within  the  shell  of  our  Earth,  and  in- 
tended them  for  our  use.      These  considerations 
amount  to  little  less  than  a  positive  proof,  that  all  the 
planets  are  inhabited  ;  for  if  they  be  not,  why  all  this 
care  in  furnishing  them  with  so  many  moons,  to 
supply  those  with  light  which  are  at  the  greater  dis- 
tances from  the  Sun?  Do  we  not  see  that  the  farther 
a  planet  is  from  the  Sun,  the  greater  apparatus  it 
has  for  that  purpose  ?  save  only  Mars,  which  being 
but  a  small  planet,  may  have  moons  too  small  to  be 
seen  by  us.     We  know  that  the  Earth  goes  round 
the  Sun,  and  turns  round  its  own  axis,  to  produce 
the  vicissitudes  of  summer  and  winter  by  the  former, 
and  of  day  and  night  by  the  latter  motion,  for  the 
benefit  of  its  inhabitants.     May  we  not  then  fairly 
conclude,  by  parity  of  reason,  that  the  end  or  de- 
sign of  all  the  other  planets  is  the  same  ?  and  is  not 
this  agreeable  to  the  beautiful  harmony  which  exists 
throughout  the  universe  ?  Surely  it  is :  and  this  con- 


Of  the  Solar  System.  67 

sideration  must  raise  in  us  the  most  magnificent  ideas  plate  r: 
of  the  SUPREME  BEING;  who  is  every  where, 
and  at  all  times  present ;  displaying  his  power,  wis- 
dom and  goodness,  among  all  his  creatures ;  and  dis- 
tributing happiness  to  innumerable  ranks  of  various 
beings ! 

87.  In  Fig.  II.  we  have  a  view  of  the  proportion-  Fig.  n.  , 
al  breadth  of  the  Sun's  face  or  disc,  as  seen  from  j?°^a£e 
the  different  planets.      The  Sun  is  represented  No.  pears  to 
1,  as  seen  from  Mercury  ;  No.  2,  as  seen  from  Ve-^  differ-. 
nus;  No.   3,  as  seen  from  the  Earth;  No.  4,  aSets.P 
seen  from  Mars ;  No.  5,  as  seen  from  Jupiter ;  and 

No.  6,  as  seen  from  Saturn. 

Let  the  circle  B  be  the  Sun,  as  seen  from  any  pla-  Fig.  in. 
net  at  a  given  distance :  to  another  planet,  at  double 
that  distance,  the  Sun  will  appear  just  of  half  that 
breadth,  as  A  ;  which  contains  only  one  fourth  part 
of  the  area  or  surface  of  B.  For  all  circles,  as  \vell 
as  square  surfaces,  are  to  one  another  as  the  squares 
of  their  diameters  or  sides.  Thus  the  square  A  is  Fl£' lv  * 
just  half  as  broad  as  the  squared;  and  yet  it  is  plain 
to  sight,  that  B  contains  four  times  as  much  sur- 
face as  A.  Hence,  by  comparing  the  diameters  of 
the  above  circles  (Fig.  II.)  together,  it  will  be  found 
that  in  round  numbers,  the  Sun  appears  7  times 
larger  to  Mercury  than  to  us,  90  times  larger  to  us 
than  to  Saturn,  and  630  times  as  large  to  Mercury 
as  to  Saturn. 

88.  In  Fig.  V.  we  have  a  view  of  the  magnitudes  Fig.  v. 
of  the  planets,  in  proportion  to  each  other,  and  to  a 
supposed  globe  of  two  feet  diameter  for  the  Sun. 

The  Earth  is  27  times  as  large  as  Mercury,  very  Propor- 
little  larger  than  Venus,  5  times  as  large  as  Mars;  J^fand 
but  Jupiter  is  1049  times  as  large  as  the  Earth,  Sa-  distances 
turn  586  times   as    large,  exclusive   of  his  ring; 
and  the  Sun  is  877  thousand  650  times  as  large  as 
the  Earth.     If  the  planets  in  this  figure  were  set  at 
».heir  due  distances  from  a  Sun  of  two  feet  diame- 
ter, according  to  their  proportionable  magnitudes, 
as  in  our  system,  Mercury  would  be  28  yards  from 
the  Sun's  centre ;  Venus  51  yards  1  foot ;  the  Earth 


<>8  Of  the  Solar  Systenu     ' 

Plate L  70  yards  2  feet;  Mars  107  yards  2  feet ;  Jupiter 
370  yards  2  feet ;  and  Saturn  760  yards  2  feet.  The 
comet  of  the  year  1680,  at  its  greatest  distance, 
10  thousand  760  yards.  Jn  this  proportion,  the 
Moon's  distance  from  the  centre  of  the  Earth  would 
be  only  7£  inches. 

AnideaoF  89.  To  assist  the  imagination  in  forming  an  idea 
their  dis-  of  the  vast  distances  of  the  Sun,  planets  and  stars, 
:es*  let  us  suppose  that  a  body  projected  from  the  Sun 
should  continue  to  fly  with  the  swiftness  of  a  cannon 
ball,  /.  e.  480  miles  every  hour ;  this  body  would 
reach  the  orbit  of  Mercury,  in  7  years  221  days; 
of  Venus,  in  14  years  8  days;  of  the  Earth,  in  19 
years  91  days;  of  Mars,  in  29  years  85  days;  of 
Jupiter,  in  100  years  280  days;  of  Saturn,  in  184 
years  240  days;  to  the  comet  of  1680,  at  its  great- 
est distance  from  the  Sun,  -in  2660  years;  and  to 
the  nearest  fixed  stars,  in  about  7  million  600  thou- 
sand years. 

Why  the  90.  As  the  Earth  is  not  in  the  centre  of  the  orbits 
planets  jn  which  the  planets  move,  they  come  nearer  to  it 
greater  andgofartherfrom.it,  at  different  times;  on  which 
and  less  at  account  they  appear  greater  and  less  by  turns. — •• 
times611  Hence,  the  apparent  magnitudes  of  the  planets  arc 
not  always  a  certain  rule  to  know  them  by. 

91.  Under  fig.  III.  are  the  names  and  characters 
of  the  twelve  signs  of  the  zodiac,  which  the  reader 
should  be  perfectly  well  acquainted  with;  so  as  to  know 
Fi  L  the  characters  without  seeing  the  names.  Each  sign 
contains  30  degrees,  as  in  the  circle  bounding  the 
solar  system;  to  which  the  characters  of  the  signs 
are  set  in  their  proper  places. 

The  com-  92.  The  COMETS  are  solid  opaque  bodies,  with 
ns-  long  transparent  trains  or  tails,  issuing  from  that 
side  which  is  turned  away  from  the  Sun.  They 
move  about  the  Sun  in  very  eccentric  ellipses ;  and 
are  of  a  much  greater  density  than  the  Earth ;  for 
some  of  them  are  heated  in  every  period  to  such  a 
degree,  as  would  vitrify  or  dissipate  any  substance 
known  to  us.  Sir  ISAAC  NEWTON  computed  the 


Of  the  Solar  System.  69 


heat  of  the  comet  which  appeared  in  the  year  1680, 
when  nearest  the  Sun,  to  be  2000  times  hotter  than 
red-hot  iron  ;  and  that  being  thus  heated,  it  must  re- 
tain its  heat  until  it  comes  round  again  ;  although  its 
period  should  be  more  than  twenty  thousand  years  ; 
though  it  is  computed  to  be  only  575.  The  method 
of  computing  the  heat  of  bodies,  keeping  at  any 
known  distance  from  the  Sun,  so  far  as  their  heat 
depends  on  the  force  of  the  Sun's  rays,  is  very  easy  ; 
and  shall  be  explained  in  the  eighth  chapter. 

93.  Part  of  the  paths  of  three  comets  is  delineat-  F1£-  I- 
ed  in  the  scheme  of  the  solar  system,  and  the  years 
marked  in  which  they  made  their  appearance.  —  - 
There  are,  at  least,  21  comets  belonging  to  our  sys-  They 
tern,  moving  in  all  sorts  of  directions  ;  and  all  Ao^SJ^wS? 
which  have  been  observed,  have  moved  through  theofthepia- 
ethereal  regions  and  the  orbits  of  the  planets,  with-  pets  af® 

rr      •  i  MI  •    ,  •       ,1      •  not  SOlld. 

out  suffering  the  least  sensible  resistance  in  their  mo- 
tions ;  which  plainly  proves  that  the  planets  do  not 
move  in  solid  orbits.  Of  all  the  comets,  the  periods  The  peri. 
of  the  above  mentioned  three  only  are  known  with  tinware 
any  degree  of  certainty.  The  first  of  these  comets  known. 
appeared  in  the  years  1531,  1607,  and  1682;  and 
is  expected  to  appear  again  in  the  year  1758,  and 
every  75th  year  afterward.  The  second  of  them 
appeared  in  1532,  and  1661,  and  may  be  expected 
to  return  in  1789,  and  every  129th  year  afterward. 
The  third,  having  last  appeared  in  1680,  and  its 
period  being  no  less  than  575  years,  cannot  return 
until  the  year  2225.  This  comet,  at  its  greatest 
distance,  is  about  eleven  thousand  two  hundred  mil- 
lions, of  miles  from  the  Sun  ;  and  at  its  least  dis- 
tance n\>mthe  Sun's  centre,  which  is  49,000  miles, 
is  within  less  than  a  third  part  of  the  Sun's  'semi-  di- 
ameter from  his  surface.  In  that  part  of  its  orbit 
which  is  nearest  the  Sun,  it  flies  with  the  amazing 
swiftness  of  880,000  miles  in  an  hour  ;  and  the  Sun, 
as  seen  from  it,  appears  a  hundred  degrees  in  breadth  ; 
consequently  40  thousand  times  as  large  as  he  ap- 


70  Of  the  Solar  System. 

They  pears  to  us.  The  astonishing  length  that  this  comet 
starTto  be  runs  out  mto  empty  space,  suggests  to  our  minds 
at  im-  an  idea  of  the  vast  distance  between  the  Sun  and 
t^e  nearest  fixed  stars;  of  whose  attractions  all  the 
comets  must  keep  clear,  to  return  periodically,  and  go 
round  the  Sun ;  and  it  shews  us  also,  that  the  near- 
est stars,  which  are  probably  those  that  seem  the 
largest,  are  as  big  as  our  Sun,  and  of  the  same  na- 
ture with  him;  otherwise,  they  could  not  appear  so 
large  and  bright  to  us  as  they  do  at  such  an  im- 
mense distance, 

inferenc-  94*  ^ie  extreme  neat>  the  dense  atmosphere,  the 
es  drawn  gross  vapours,  the  chaotic  state  of  the  comets,  seem 
?t  *irstsignt  to  m^icate  them  altogether  unfit  for  the 
"  purposes  of  animal  life,  and  a  most  miserable  habi- 
tation for  rational  beings ;  and  therefore  some*  are 
of  opinion  that  they  are  so  many  hells  for  torment- 
ing the  damned  with  perpetual  vicissitudes  of  heat 
and  cold.  But  when  we  consider,  on  the  other  hand, 
the  infinite  power  and  goodness  of  the  Deity  ;  the 
latter  inclining,  the  former  enabling  him  to  make 
creatures  suited  to  all  states  and  circumstances ;  that 
matter  exits  only  for  the  sake  of  intelligent  beings; 
and  that  wherever  we  find  it,  we  always  find  it  preg- 
nant with  life,  or  necessarily  subservient  thereto ; 
the  numberless  species,  the  astonishing  diversity  of 
animals  in  earth,  air,  water,  and  even  on  other  ani- 
mals ;  every  blade  of  grass,  every  tender  leaf,  eve- 
ry natural  fluid,  swarming  with  life;  and  every  one 
of  these  enjoying  such  gratifications  as  the  nature  and 
state  of  each  requires :  when  we  reflect,  moreover, 
that  some  centuries  ago,  till  experience  undeceived 
us,  a  great  part  of  the  Earth  was  adjudged  uninhabi- 
table; the  torrid  zone,  by  reason  of  excessive  heat,  and 
the  two  frigid  zones  because  of  their  intolerable  cold ; 
it  seems  highly  probable,  that  such  numerous  and 

*  Mr.  WHISTON,  in  his  Astronomical  Principles  of  Religion. 


Of  the  Solar  System.  71 

large  masses  of  durable  matter  as  the  comets  are, 
however  unlike  they  be  to  our  Earth,  are  not  des- 
titute of  beings  capable  of  contemplating  with 
wonder,  and  acknowledging  with  gratitude,  the 
wisdom,  symmetry,  and  beauty  of  the  creation ; 
which  is  more  plainly  to  be  observed  in  their  ex- 
tensive tour  through  the  heavens,  than  in  our  more 
confined  circuit.  If  farther  conjecture  be  per- 
mitted, may  we  not  suppose  them  instrumental  in 
recruiting  the  expended  fuel  of  the  Sun ;  and  sup- 
plying the  exhausted  moisture  of  the  planets? 
However  difficult  it  may  be,  circumstanced  as  we 
are,  to  find  out  their  particular  destination,  this  is 
an  undoubted  truth,  that  wherever  the  Deity  ex- 
erts his  power,  there  he  also  manifests  his  wisdom 
and  goodness. 

95.  THE  SOLAR  SYSTEM,  here  described,™^- 
is  not  a  late  invention ;  for  it  was  known  and  taught  ancient y 
by  the  wise   Samiari  philosopher   PYTHAGORAS, and de- 
and  others  among  the  ancients  :  but  in  latter  times  ™°nstra* 
was  lost,  till  the  15th  century,  when  it  was  again 
restored  by  the  famous  Polish  philosopher,  NICHO- 
LAUS  COPERNICUS,   born  at  Thorn  in  the  year 
1473.     In  this  he  was  followed  by  the  greatest  ma- 
thematicians and  philosophers  that  have  since  lived ; 

as  KEPLER,GALILEO,DESCARTES,GASSENDUS, 
and  Sir  ISAAC  NEWTON  ;  the  last  of  whom  has  es- 
tablished this  system  on  such  an  everlasting  founda- 
tion of  mathematical  and  physical  demonstration, 
as  can  never  be  shaken ;  and  none  who  understand 
him  can  hesitate  about  it. 

96.  In  the  Ptolemean  system,  the  Earth  was  sup-  ThePtole- 
posed  to  be  fixed  in  the  centre  of  the  universe ; 

and  the  Moon,  Mercury,  Venus,  the  Sun,  Mars, 
Jupiter,  and  Saturn,  to  move  round  the  Earth. 
Above  the  planets,  this  hypothesis  placed  the  fir- 
mament of  stars,  and  then  the  two  crystalline 
spheres :  all  which  were  included  in  and  received 
motion  from  the  primum  mobile,  which  constantly 

K 


72  Of  the  Solar  System. 

revolved  about  the  Earth  in  24  hours  from  east  to 
west.  But  as  this  rude  scheme  was  found  inca- 
pable of  standing  the  test  of  art  and  observation,  it 
was  soon  rejected  by  all  true  philosophers;  not- 
withstanding the  opposition  and  violence  of  blind 
and  zealous  bigots. 

The  Ty.        97.  The  Tychonic  system  succeeded  the  Ptolo- 
sys°tem      mean,  but  was  never  so  generally  received.    In  this 
partly       the  Earth  was  supposed  to  stand  still  in  the  centre 
*Trd  and  °f  ^ie  uniyerse  or  firmament  of  stars,  and  the  Sun 
false.        to  revolve  about  it  every  24  hours  ;  the  planets, — 
Mercury,  Venus,  Mars,  Jupiter,  and  Saturn,  go- 
ing round  the  Sun  in  the  times  already  mentioned. 
But  some  of  TYCHO'S  disciples  supposed  the  Earth 
to  have  a  diurnal  motion  round  its  axis,  and  the 
Sun  with  all  the  above  planets  to  go  round  the 
Earth  in  a  year;    the  planets  moving   round  the 
Sun  in  the  aforesaid  times.     This  hypothesis  being 
partly  true  and  partly  false,  was  embraced  by  few  ; 
and  soon  gave  way  to  the  only  true  and  rational  sys- 
tem, restored  by  COPERNICUS,  and  demonstrated 
by  Sir  ISAAC  NEWTON. 

98.  To  bring  the  foregoing  particulars  into  one 
point  of  view,  with  several  others  which  follow, 
concerning  the  periods,  distances,  magnitudes,  £sfc. 
of  the  planets,  the  following  table  is  inserted. 


rdi 


aas, 

.  .  QCj* 


r£e$ 
£§•£§ 

?g»S-2:er. 

***g 

{^g  H?.rt 

i'sf? 

^  c-rt^ 

ifs-g 
f"s 

•   3  55  o 
5-1  S  P 

Sf  ?a 

S2.|-S  S 
"4  S3 

22  2!g- 

?»53 

*I|? 

as  ft  &  n> 

3    co    p    3 

^o  3  p- 

P?M' 

«2J| 
Zfl 

^2i 

>§0^ 
w  p-^x 

«  ^ffi* 

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^•5  g  t 

^'S'rt  S, 

w.  -  JS  n» 

w  Js-^ 
2  ^£  £ 

^s^-r 

es-p*«  & 

p    ^    3   n> 

03    t~*  r+  ,» 

UN 

13  ^      r*    O 

S^I 
4"^ 

HM 

i*.|£ 

?g^s 

.8-nfg1 
8L^  §? 

I  S.2,5' 
-gSS: 

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rM 

&Sni 

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f|38 

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g?5| 

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e  po'rt 
&5?? 


c 

o  £-2 


03  M  t-  o>  u, 

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zr.  p.  >ri 
p*orcj  o  -J 


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s-?Ss 
5s,  1-1 


to 
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tO  tO        X- 


O3  tO  Or?  CO  O» 
Ort  Cft  OC  tO  4*- 


§ooocootoo-»o 
oo*>-oosooo 

OOOOOOOOO 


—  , 


3  ~^  o>  u,  ^  03  to  »- 


f 


: 

D    ps 


f      3" 


iO  M  03  *- 

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tr»         H*  CD 
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o  <o  u»  ^  >-* 


5-9  n  rf  ^ 

n>  £.£  oc£ 

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Saturn. 


n 


£  o' 


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OO 

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»-.  CO  *-        JO  03  to 


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- 


O  O  O  O  O  O  O 

<C  O  O  O  O  O  O 

o  o  o  o  o  o  o 


<D  O  O  O  O 

o  o  o  o  o 
o  o  o  o  o 


Ntia  03  ^  M 

O  OJ  Ut  C/J  K-*  M  >-»  tO 


o  o  o  o  o  o  o  o 
oooooooo 


ooooo- o 


o  to  t-i  K*  o> 

O     O     0     O     0 


*»•  OO  to  Ort  H* 

q»  o  o  to  oo 


o  4^ 


H-   tO    tO 
O3  "^  -v|  O 

O     0     O     O 


>-*  tO         >-*  "J 

to  i—  "-j  -vj  -• 

0000^ 

*  ;r 
»  . 


^  M  to  H* 
^  oo  <o  ^» 


S^  S'  3. 
-    3 


3        . 


ace  of  i 
phelion 


, 

I  PI 
' 


the  Period 
distan 


Revolutions,  Magnitudes,  &.c.  of  t 
from  the  SUN,  as  determined  from 


Planets,  on  the  Sup 
servations  of  the  tran 


f! 

"I." 

5'  CA! 


llax  being  10" 
761,  see  §  194. 


74  The  Cop  ernican  System  demonstrated  to  be  true. 


CHAP.  III. 

The  COPERNICAN  SYSTEM  demonstrated  to 
be  true. 

ndmo    99  '  "\yfATTER  is  of  itself  inactive,  and  indif- 
tion.  xVA  ferent  to  motion  or  rest.    A  body  at  rest 

can  never  put  itself  in  motion  ;  a  body  in  motion 
can  never  stop  or  move  slower  of  itself.  Hence, 
when  we  see  a  body  in  motion,  we  conclude  that  some 
other  substance  must  have  given  it  that  motion  ; 
when  we  see  a  body  fall  from  motion  to  rest  we  con- 
clude that  has  some  other  body  or  cause  stopt  it. 

100.  All  motion  is  naturally  rectilineal.  A  bullet 
thrown  by  the  hand,  or  discharged  from  a  cannon, 
would  continue  to  move  in  the  same  direction  it  re- 
ceived at  first,  if  no  other  power  diverted  its  course. 
Therefore,  when  we  see  a  body  moving  in  a  curve  of 
whatever  kind,  we  conclude  it  must  be  acted  upon 
by  two  powers  at  least  :  one  to  put  it  in  motion,  and 
another  drawing  it  off  from  the  rectilineal  course 
which  it  would  otherwise  have  continued  to  move 
in. 

Gravity  101.  The  power  by  which  bodies  fall  toward  the 
IrtraWe"  ^art^'  *s  ca^e(l  gravity  or  attraction.  By  this 
power  in  the  Earth  it  is,  that  all  bodies  on  what- 
ever side,  fall  in  lines  perpendicular  to  its  surface. 
On  opposite  parts  of  the  Earth,  bodies  fall  in  op- 
posite directions  ;  —  all  toward  the  centre,  where  the 
whole  force  of  gravity  is,  as  it  were,  accumulated. 
By  this  power  constantly  acting  on  bodies  near  the 
Earth,  they  are  kept  from  leaving  it  altogether; 
and  those  on  its  surface  are  kept  there  on  all  sides, 
so  that  they  cannot  fall  from  it.  Bodies  thrown 
with  any  obliquity  are  drawn,  by  this  power,  from 
a  straight  line  into  a  curve,  until  they  fall  to  the 
ground  :  the  greater  the  force  by  which  they  are 
thrown,  the  greater  is  the  distance  they  are  carried 
before  they  fall.  If  we  suppose  a  body  carried  se- 


The  Copernican  System  demonstrated  to  be  true.  75 

veral  miles  above  the  Earth,  and  there  projected  in 
a  horizontal  direction,  with  so  great  a  velocity,  that 
it  would  move  more  than  a  semidiameter  of  the 
Earth  in  the  time  it  would  take  to  fall  to  the  Earth 
by  gravity  ;  in  that  case,  if  there  were  no  resisting 
medium  in  the  way,  the  body  would  not  fall  to  the 
Earth  at  all,  but  continue  to  circulate  round  the 
Earth,  keeping  always  the  same  path,  and  returning 
to  the  point  from  whence  it  was  projected,  with  the 
same  velocity  as  at  first. 

102.  We  find  that  the  Moon  moves  round  the  Earth  Projectile 
in  an  orbit  nearly  circular.     The  Moon  therefore 


must  be  acted  on  by  two  powers  or  forces  ;  one,  bie. 
which  would  cause  her  to  move  in  a  right  line; 
another,  bending  her  motion  from  that  line  into  a 
curve.  This  attractive  power  must  be  seated  in 
the  Earth  ;  for  there  is  no  other  body  within  the 
Moon's  orbit  to  draw  her.  The,  attractive  power 
of  the  Earth  therefore  extends  to  the  Moon  ;  and, 
in  combination  with  her  projectile  force,  causes  her 
to  move  round  the  Earth,  in  the  same  manner  as  the 
circulating  body  above  supposed. 

103.  The  moons  of  Jupiter  and  Saturn  are  ob-  The  Sun 
served  to  move  round  their  primary  planets  :  there- 

fore  there  is  an  attractive  power  in  these  planets,  each 
All  the  planets  move  round  the  Sun,  and  respect  itother> 
for  their  centre  of  motion  :  therefore  the  Sun  must 
be  endowed  with  an  attracting  power,  as  well  as  the 
Earth  and  planets.     The  like  may  be  proved  of  the 
comets.  So  that  all  the  bodies  or  matter  of  the  solar 
system,  are  possessed  of  this  power;  and  so  per- 
haps  is  all  matter  universally. 

104.  As  the  Sun  attracts  the  planets  with  their 
satellites,  and  the  Earth  the  Moon  ;  so  the  planets 
and  satellites  re-attract  the  Sun,  and  the  Moon  the 
Earth;    action  and    re-action  being  always  equal. 
This   is   also  confirmed   by  observation  ;    for  the 
Moon  raises  tides  in  the  ocean,  and  the  satellites 
and  planets  disturb  one  another's  motions. 


76  The  Copernican  System  demonstrated  to  be  true. 

105.  Every  particle  of  matter  being  possessed  of 
an  attracting  power,  the  effect  of  the  whole  must 
be  in  proportion  to  the  number  of  attracting  parti- 
cles :  that  is,  to  the  quantity  of  matter  in  the  body. 
This  is  demonstrated  from  experiments  on  pendu- 
lums :  for,  when  they  are  of  equal  lengths,  whatever 
their    weights    be,    they    always   vibrate   in   equal 
times.     Now,  if  one  be  double  the  weight  of  an- 
other, the  force  of  gravity  or  attraction  must  be 
double  to  make  it  oscillate  with  the  same  celerity ; 
if  one  have  thrice  the  weight  or  quantity  of  matter 
of  another,  it  requires  thrice  the  force  of  gravity  to 
make  it  move  with  the  same  celerity.     Hence  it  is 
certain,  that  the  power  of  gravity  is  always  propor- 
tional to  the  quantity  of  matter  in  bodies,  whatever 
may  be  their  magnitudes  or  figures. 

106.  Gravity  also,  like  all  other  virtues  or  ema- 
nations, either  drawing  or  impelling  a  body  toward 
the  centre,  decreases  as  the  square  of  the  distance 
increases:  that  is,  a  body  at  twice  the  distance  attracts 
another  with  only  a  fourth  part  of  the  force ;  at  four 
times  the  distance,  with  a  sixteenth  part  of  the  force, 
&c.     This  too  is  confirmed  from  observation,  by 
comparing  the  distance  which  the  MOOR  falls  in  a 
minute  from  a  right  line  touching  her  orbit,  with  the 
space  which  bodies  near  the  Earth  fall  in  the  same 
time :  and  also  by  comparing  the  forces  which  retain 
Jupiter's  moons  in  their  orbits:  as  will  be  more  fully 
explained  in  the  seventh  chapter. 

£onVand~        107'    Tlie   mutual  Attraction  of  bodies  may  be 

projection  exemplified   by   a   boat  and  a  ship  on  the  water, 

exempli-  tied  together  by  a  rope.     Let  a  man  either  in  the 

ship  or  boat  pull  the  rope  (it  is  the  same  in  effect  at 

which  end  he  pulls,  for  the  rope  will  be  equally 

stretched   throughout)   the  ship  and   boat  will  be 

drawn  toward  one  another ;  but  with  this  difference, 

that  the  boat  will  move  as  much  faster  than  the  ship, 

as  the  ship  is  heavier  than  the  boat.     Suppose  the 

boat  as  heavy  as  the  ship,  and  they  will  draw  one 


The  Copernican  System  demonstrated  to  be  true.  77 

another  equally,  (setting  aside  the  greater  resistance 
of  the  water  on  the  larger  body)  and  meet  in  the 
middle  of  the  first  distance  between  them.     If  the 
ship  be  a  thousand  or  ten  thousand  times  heavier 
than  the  boat,  the  boat  will  be  drawn  a  thousand  or 
ten  thousand  times  faster  than  the  ship ;  and  meet 
proportionably  nearer  the  place  from  which  the  ship 
set  out.     Now,  while  one  man  pulls  the  rope,  en- 
deavouring to  bring  the  ship  and  boat  together,  let 
another  man  in  the  boat,  endeavour  to  row  it  off  side- 
ways, or  at  right  angles  to  the  rope  ;  and  the  former, 
instead  of  being  able  to  draw  the  boat  to  the  ship, 
will  find  it  enough  for  him  to  keep  the  boat  from 
going  further  off;  while  the  latter  endeavouring  to  row 
off  the  boat  in  a  straight  line,  will,  by  means  of  the 
other's  pulling  it  toward  the  ship,  row  the  boat  round 
the  ship  at  the  rope's  length  from  her.     Here  the 
power  employed  to  draw  the  ship  and  boat  to  one 
another  represents  the  mutual  attraction  of  the  Sun 
and  planets  by  which  the  planets  would  fall  freely  to- 
ward the  Sun  with  a  quick  motion ;  and  would  also 
in  falling  attract  the  Sun  toward  them.     And  the 
power  employed  to  row  off  the  boat,  represents  the 
projectile  force  impressed  on*the  planets,  at  right 
angles,  or  nearly  so,  to  the  Sun's  attraction;    by 
which  means  the  planets  move  round  the  Sun,  and 
are  kept  from  falling  to  it.     On  the  other  hand,  if  it 
be  attempted  to  make  a  heavy  ship  go  round  a  light 
boat,  they  will  meet  sooner  than  the  ship  can  get 
round  ;  or  the  ship  will  drag  the  boat  after  it. 

108.  Let  the  above  principles  be  applied  to  the 
Sun  and  Earth ;  and  they  will  evince,  beyond  a  pos- 
sibility of  doubt,  that  the  Sun,  not  the  Earth,  is  the 
centre  of  the  system ;  and  that  the  Earth  moves 
round  the  Sun  as  the  other  planets  do. 

For,  if  the  Sun  move  about  the  Earth,  the 
Earth's  attractive  power  must  draw  the  Sun  toward 
it,  from  the  line  of  projection,  so  as  to  bend  its 
motion  into  a  curve.  But  the  Sun  being  at  least 


78  The  Copernican  System  demonstrated  to  be  true. 

227  thousand  times  as  heavy  as  the  Earth,  being  so 
much  heavier  as  its  quantity  of  matter  is  greater,  it 
must  move  227  thousand  times  as  slowly  toward  the 
Earth,  as  the  Earth  does  toward  the  Sun ;  and  con- 
sequently the  Earth  would  fall  to  the  Sun  in  a  short 
time,  if  it  had  not  a  very  strong  projectile  motion  to 
carry  it  off.  The  Earth  therefore,  as  well  as  e very- 
other  planet  in  the  system,  must  have  a  rectilineal  im- 
srurdity "ofPu^se»  to  prevent  its  falling  to  the  Sun.  To  say, 
supposing  that  gravitation  retains  all  the  other  planets  in  their 
earth  orbits,  without  affecting  the  Earth,  which  is  placed 
between  the  orbits  of  Mars  and  Venus,  is  as  absurd 
as  to  suppose  that  six  cannon  bullets  might  be  pro- 
jected upward  to  different  heights  in  the  air ;  and 
that  five  of  them  should  fall  down  to  the  ground, 
but  the  sixth,  which  is  neither  the  highest  nor  the 
lowest  should  remain  suspended  in  the  air  without 
falling,  and  the  Earth  move  round  about  it. 

109.  There  is  no  such  thing  in  nature  as  a  heavy 
body  moving  round  a  light  one,  as  its  centre  of  mo- 
tion.   A  pebble  fastened  to  a  mill-stone,  by  a  string, 
may,    by  an  easy  impulse,    be  made  to  circulate 
round  the  mill-stone  ;  but  no  impulse  whatever  can 
make  a  mill- stone  circulate  round  a  loose  pebble  ; 
for  the  mill- stone  would  go  off,  and  carry  the  pebble 
along  with  it. 

1 10.  The  Sun  is  so  immensely  greater  and  hea- 
vier than  the  Earth,*  that  if  he  were  moved  out  of 
his  place,  not  only  the  Earth,  but  all  the  other  pla- 
nets, if  they  were  united  into  one  mass,  would  be 
carried  along  with  the  Sun,  as  the  pebble  would  be, 
with  the  mill-stone. 

111.  By  considering  the  law  of  gravitation  which 
takes  place  throughout  the  solar  system,  in  another 
light,    it   will   be  evident,  that  the   Earth   moves 
round  the  Sun  in  a  year ;  and  not  the  Sun  round 
the  Earth.     It  has  been  shewn  (§   106)   that  the 

*  As  will  be  demonstrated  in  the  ninth  chapter. 


The  Copermcan  System  demonstrated  to  be  true.  79 

power  of  gravity  decreases  as  the  square  of  the  dis-  The  har- 
tance  increases ;  and  from  this  it  follows,  with  mathe-  J^cdeg. 
matjcal  certainty,    that  when  two  or  more  bodies  tial  mo. 
move  round  another  as  their  centre  of  motion,  thetlons* 
squares  of  their  periodic  times  Will  be  to  one  another 
in  the  same  proportion  as  the  cubes  of  their  distances 
from  the  central  body.     This  holds  precisely  with 
regard  to  the  planets  round  the  Sun,  and  the  satel- 
lites round  the  planets  ;  the  relative  distances  of  all 
which  are  well  known.    But,  if  we  suppose  the  Sun 
to  move  round  the  Earth,  and  compare  its  period 
with  the  Moon's  by  the  above  rule,  it  will  be  found 
that  the  Sun  would  take  no  less  than  173,510  days 
to  move  round  the  Earth ;  in  which  case  our  year 
would  be  475  times  as  long  as  it  now  is.     To  this 
we  may  add,  that  the  aspects  of  increase  and  de- 
crease of  the  planets,  the  times  of  their  seeming  to 
stand  still,  and  to  move  direct  and  retrograde,  an- 
swer precisely  to  the  Earth's  motion  ;  but  not  at  .all 
to  the  Sun's,  without  introducing  the  most  absurd 
and  monstrous  suppositions,  which  would  destroy  all 
harmony,  order,  and  simplicity  in  the  system.  More- 
over, if  the  Earth  be  supposed  to  stand  still,  and  the 
stars  to  revolve  in  free  space  about  the  Earth  in  24 
hours,  it  is  certain  that  the  forces  by  which  the  stars 
revolve  in  their  orbits  are  not  directed  to  the  Earth, 
but  to  the  centres  of  the  several  orbits ;  that  is,  of  the 
several  parallel  circles  which  the  stars  on  different  The  ab- 
sides  of  the  equator  describe  every  day ;  and  the  like  JU"1^  °f 
inferences  may  be  drawn  from  the  supposed  diurnal  the  stars S 
motion  of  the  planets,  since  they  are  never  in  the*n^P|a- 
cquinoctial  but  twice  in  their  courses  with  regard  to  move 
the  starry  heavens.     But,  that  forces  should^be  di- round  the 
rected  to  no  central  body,  on  which  they  physically  Earth' 
depend,  but  to  innumerable  imaginary  points  in  the 
axis  of  the  Earth  produced  to  the  poles  of  the  hea- 
vens, is  a  hypothesis  too  absurd  to  be  allowed  of 
by  any  rational  creature.     And  it  is  still  more  ab* 

L 


80  The  Copernican  System  demonstrated  to  be  true. 

surd  to  imagine  that  these  forces  should  increase  ex- 
actly in  proportion  to  the  distances  from  this  axis ; 
for  that  is  an  indication  of  an  increase  to  infinity ; 
whereas  the  force  of  attraction  is  found  to  decrease 
in  receding  from  the  fountain  from  whence  it  flows. 
But  the  farther  any  star  is  from  the  quiescent  pole, 
the  greater  must  be  the  orbit  which  it  describes ;  and 
yet  it  appears  to  go  round  in  the  same  time  as  the 
nearest  star  to  the  pole  does.  And  if  we  take  into 
consideration  the  two-fold  motion  observed  in  the 
stars,  one  diurnal  round  the  axis  of  the  Earth  in  24 
hours,  and  the  other  round  the  axis  of  the  ecliptic  in 
25920  years,  §  251,  it  would  require  an  explication 
of  such  a  perplexed  composition  of  forces,  as  could 
by  no  means  be  reconciled  with  any  physical  theory. 

objec-          112.  There  is  but  one  objection  of  any  weight 
against     tnat  can  ^e  made  against  the  Earth's  motion  round 
the          the  Sun,  which  is,  that  in  opposite  points  of  the 
motionan-  F'artn's  orbit,  its  axis,  which  always  keeps  a  paral- 
swered.    lei  direction,  would  point  to  different  fixed  stars ; 
which  is  not  found  to  be  fact.     But  this  objection 
is  easily  removed,  by  considering  the  immense  dis- 
tance of  the  stars  in  respect  to  the  diameter  of  the 
Earth's  orbit ;  the  latter  being  no  more  than  a  point 
when  compared  to  the  former.     If  we  lay  a  ruler  on 
the  side  of  a  table,  and  along  the  edge  of  the  ruler 
view  the  top  of  a  spire  at  ten  miles  distance,  and 
then  lay  the  ruler  on  the  opposite  side  of  the  table 
in  a  parallel  situation  to  what  it  had  before,  the  spire 
will  still  appear  along  the  edge  of  the  ruler,  because 
our  eyes,  even  when  assisted  by  the  best  instru- 
ments, are  incapable  of  distinguishing  so  small  a 
change  at  so  great  a  distance. 

113.  Dr.  BRADLEY  found,  by  a  long  series  of  the 
most  accurate  observations,  that  there  is  a  small  ap- 
parent motion  of  the  fixed  stars,  occasioned  by  the 
aberration  of  their  light,  and  so  exactly  answering  to 


The  Coper mean  System  demonstrated  to  be  true.  81 

an  annual  motion  of  the  Earth,  as  evinces  the  same, 
even  to  a  mathematical  demonstration.  Those  who 
are  qualified  to  read  the  Doctor's  modest  account  of 
this  great  discovery,  may  consult  the  Philosophical 
Transactions,  No.  406.  Or  they  may  find  it  treated 
of  at  large  by  Drs.  SMITH*,  LoNcf,  DESAGU- 
LiERsf,  RUTHERFURTH||,  Mr.  MACLAURIN,  Mr. 
SIMPSON^,  and  M.  DE  LA  CAILLE**. 

114.  It  is  true  that  the  Sun  seems  to  change  hiswhy the 

11-1  i  11  Sun  ap- 

place  daily,  so  as  to  make  a  tour  round  the  starry  pearsto 
heavens  in  a  year.     But  whether  the  Sun  or  Earth  change 
moves,  this  appearance  will  be  the  same;  for,  whenhls  place' 
the  Earth  is  in  any  part  of  the  heavens,  the  Sun  will 
appear  in  the  opposite.     And  therefore  this  appear- 
ance can  be  no  objection  against  the  motion  of  the 
Earth. 

115.  It  is  well  known  to  every  person  who  has 
sailed  on  smooth  water,  or  been  carried  by  a  stream 
in  a  calm,  that,  howevel*  fast  the  vessel  goes,  he 
does  not  feel  its  progressive  motion.     The  motion 
of  the  Earth  is  incomparably  more  smooth  and  uni- 
form than  that  of  a  ship,  or  any  machine  made  and 
moved  by  human  art :  and  therefore  it  is  not  to  be 
imagined  that  we  can  feel  its  motion. 

116.  We  find  that  the  Sun,  and  those  planets  Th« 

on  which  there  are  visible  spots,  turn  round  their  motion3  on 
axes  :  for  the  spots  move  regularly  over  their  discs,  its  axis 
From  hence   we   may    reasonably   conclude,    that^™™' 
the  other  planets  on  which  we  see  no  spots,  and 
the  Earth,  which  is  likewise  a  planet,  have  such 
rotations.    But  being  incapable  of  leaving  fhe  Earth, 
and  viewing  it  at  a  distance,  and  its  rotation  being 
smooth  and  uniform,  we  can  neither  see  it  move 

*  Optics,  B.  I.  §  1178.  t  Astronomy,  B.  II.  §  838. 

|  Philosophy,  vol.  1.  p.  401,  |j  Account  of  Sir  Isaac  New- 

ton's PhUosoftiical  Discoveries,  B.  III.  c.  2.  §  3. 
§  Mathemat.  Essays,  p.  1.        **  Elements  d'  Astronomic*  §  381. 


82  The  Copcrnican  System  demonstrated  to  be  true. 

on  its  axis  as  we  do  the  planets,  nor  feel  ourselves 
affected  by  its  motion.  Yet  there  is  one  effect  of 
such  a  motion,  which  will  enable  us  to  judge  with 
certainty  whether  the  Earth  revolvVs  on  its  axis  or 
not.  All  globes  which  do  not  turn  round  their  axes 
will  be  perfect  spheres,  on  account  of  the  equality 
of  the  weight  of  bodies  on  their  surfaces ;  especi- 
ally of  the  fluid  parts.  But  all  globes  which  turn  on 
their  axes  will  be  oblate  spheroids ;  that  is,  their 
surfaces  will  be  higher  or  farther  from  the  centre  in 
the  equatorial  than  in  the  polar  regions ;  for,  as  the 
equatorial  parts  move  quickest,  they  will  recede  far- 
thest  from  the  axis  of  motion,  and  enlarge  the  equa- 
torial diameter.  That  our  Earth  is  really  of  this 
figure,  is  demonstrable  from  the  unequal  vibrations 
of  a  pendulum,  and  the  unequal  lengths  of  degrees 
in  different  latitudes.  Since  then  the  Earth  is  higher 
at  the  equator  than  at  the  poles,  the  sea,  which  na- 
turally runs  downward,  or  toward  the  places  which 
are  nearest  the  centre,  would  run  toward  the  polar 
regions,  and  leave  the  equatorial  parts  dry,  if  the 
centrifugal  force  of  these  parts  by  which  the  waters 
were  carried  thither  did  not  keep  them  from  return- 
ing. The  Earth's  equatorial  diameter  is  36  miles 
longer  than  its  axis. 

All  bodies      \yj .  Bodies  near  the  poles  are  heavier  than  those 
the^oie*  toward  the  equator,    because  they  are   nearer  the 
than  they  Earth's  centre,  where  the  whole  force  of  the  Earth's 
atthe    e  attraction  is  accumulated.     They  are  also  heavier, 
equator,    because  their  centrifugal  force  is  less,  on  account 
of  their  diurnal  motion  being  slower.     For  both 
these  reasons,  bodies  carried  from  the  poles  toward 
the  equator  gradually  lose  of  their  weight.     Ex- 
periments prove  that  a  pendulum  which  vibrates 
seconds  near   the  poles,   vibrates  slower  near  the 
equator ;    which  shews,    that  it  is  lighter  or  less 
attractive  there.     To  make  it  oscillate  in  the  same 
time,  it  is  fdund  necessary  to  diminish  its  length. 
By  comparing  the  different  lengths  of  pendulums 


The  Copernican  System  demonstrated  to  be  true.  83 

swinging  seconds  at  the  equator  and  at  London,  it  is 
found  that  a  pendulum  must  be  2Tis6A  lines,  or  12th 
part  of  an  inch  shorter  at  the  equator  than  at  the  poles. 

118.  If  the  Earth  turned  round  its  axis  in  84  mi- 
nutes  43  seconds,  the  centrifugal  force  would  be  S 
equal  to  the  power  of  gravity  at  the  equator ;  and  all  weight, 
bodies  there  would  entirely  lose  their  weight.     If 

the  Earth  revolved  quicker,  they  would  all  fly  off, 
and  leave  it. 

119.  A  person  on  the  Earth  can  no  more  be  sen-3"he, , 

.,,/..  -..         ,1  .  .  .        i  &artn  $ 

sible  oi  its^undisturbed  motion  on  its  axis,  than  one  motion 
in  the  cabin  of  a  ship,  on  smooth  water,  can  be  sen-cannotbe 
sible  of  the  ship's  motion  when  it  turns  gently  and  e 
uniformly  round.      It  is  therefore  no    argument 
against  the  Earth's  diurnal  motion,  that  we  do  not 
feel  it :  nor  is  the  apparent  revolutions  of  the  celes- 
tial bodies  every  day  a  proof  of  the  reality  of  these 
motions ;  for  whether  we  or  they  revolve,  the  ap- 
pearance  is   the   very   same.      A  person   looking 
through  the  cabin- windows  of  a  ship,  as  strongly 
fancies  the  objects  on  land  to  go  round  when  the 
ship  turns,  as  if  they  were  actually  in  motion. 

120.  If  we  could  translate  ourselves  from  planet 
to  planet,  we  should  still  find  that  the  stars  would 
-appear  of  the  same  magnitudes,  and  at  the  same 
distances  from  each  other,  as  they  do  to  us  on  the 
Earth,  because  the  diameter  of  the  remotest  planet's 
orbit  bears  no  sensible  proportion  to  the  distance  of 

the  stars.     But  then,  the  heavens  would  seem  tojFothedif 
revolve  about  very  different  axes;  and  con  sequent-  ne^the* 
ly,  those  quiescent  points,  which  are  our  poles  in  heavens 
the  heavens,  would  seem  to  revolve  about  other  Aroun 
points,  which,  though  apparently  in  motion  as  seen  on  differ- 
from  the  Earth,  would  be  at  rest  as  seen  from  any  ent  axes* 
other  planet.     Thus  the  axis  of  Venus  which  lies 
almost  at  right  angles  to  the  axis  of.  the  Earth, 
would  have  its  motionless  poles  in  two  opposite 
points  of  the  heavens,  lying  almost  in  our  equi- 


The  Copernican  System  demonstrated  to  be  true. 

noctial,  where  the  motion  appears  quickest;  be^ 
cause  it  is  seemingly  performed  in  the  greatest  circle. 
And  the  very  poles  which  are  at  rest  to  us,  have  the 
quickest  motion  of  all  as  seen  from  Venus.  To 
Mars  and  Jupiter,  the  heavens  appear  to  turn  round 
with  very  different  velocities  on  the  same  axis,  whose 
poles  are  about  23^  degrees  from  ours.  Were  we 
on  Jupiter,  we  should  be  at  first  amazed  at  the  rapid 
motion  of  the  heavens ;  the  Sun  and  stars  going 
round  in  9  hours  56  minutes.  Could  we  go  from 
thence  to  Venus,  we  should  be  as  much  surprised 
at  the  slowness  of  the  heavenly  motions ;  the  Sun 
going  but  once  round  in  584  hours,  and  the  stars  in 
540.  And  could  we  go  from  Venus  to  the  Moon, 
we  should  see  the  heavens  turn  round  with  a  yet 
slower  motion ;  the  Sun  in  708  hours,  the  stars  in 
655.  As  it  is  impossible  these  various  circumvo- 
lutions in  such  different  times,  and  on  such  different 
axes,  can  be  real,  so  it  is  unreasonable  to  suppose 
the  heavens  to  revolve  about  our  Earth,  more  than 
it  does  abbut  any  other  planet.  When  we  reflect 
on  the  vast  distance  of  the  fixed  stars,  to  which 
162,000,000  of  miles,  the  diameter  of  the  Earth's 
orbit,  is  but  a  point,  we  are  filled  with  amazement  at 
the  immensity  of  their  distance.  But  if  we  try  to 
frame  an  idea  of  the  extreme  rapidity  with  which  the 
stars  must  move,  if  they  move  round  the  Earth  in 
24  hours,  the  thought  becomes  so  much  too  big  for 
our  imagination,  that  we  can  no  more  conceive  it  than 
we  do  infinity  or  eternity.  If  the  Sun  were  to  go  round 
the  Earth  in  24  hours,  he  must  travel  upward  of 
300,000  miles  in  a  minute  :  but  the  stars  being  at  least 
400,000  times  as  far  from  the  Sun  as  the  Sun  is  from 
us,  those  about  the  equator  must  move  400,000  times 
as  quick.  And  all  this  to  serve  no  other  purpose 
than  what  can  be  as  fully  and  much  more  simply  ob- 
tained by  the  Earth's  turning  round  eastward,  as  on 
an  axis,  every  24  hours;  causing  thereby  an  apparent 


Objections  answered.  35 

diurnal  motion  of  the  Sun  westward,  and  bringing 
about  the  alternate  returns  of  day  and  night. 

121.  As  to  the  common  objections  against  the 
Earth's  motion  on  its  axis,  they  are  all  easily  an- 
swered, and  set  aside.  That  it  may  turn  without  be-  Earth's  di- 

,,  ,      ,  ,  ,     urnal  mo- 

ing  seen  or  felt  by  us  to  do  so,  has  been  already  tion  an- 
shewn,  §  119.  But  some  are  apt  to  imagine  that  ii  swered. 
the  Earth  turns  eastward  (as  it  certainly  does,  if  it 
turns  at  all)  a  ball  fired  perpendicularly  upward  in  the 
air  must  fall  considerably  westward  of  the  place  it 
was  projected  from.  This  objection,  which  at  first 
seems  to  have  some  weight,  will  be  found  to  have 
none  at  all,  when  we  consider  that  the  gun  and  ball 
partake  of  the  Earth's  motion ;  and  therefore  the  ball 
being  carried  forward  with  the  air  as  quick  as  the 
Earth  and  air  turn,  must  fall  down  on  the  same  place. 
A  stone  let  fall  from  the  top  of  a  main- mast,  if  it 
meet  with  no  obstacle,  falls  on  the  deck  as  near  the 
foot  of  the  mast  when  the  ship  sails  as  when  it  does 
not.  If  an  inverted  bottle  full  of  liquor,  be  hung  up 
to  the  ceiling  of  the  cabin,  and  a  small  hole  be  made 
in  the  cork  to  let  the  liquor  drop  through  on  the 
floor,  the  drops  will  fall  just  as  far  forward  on  the 
floor  when  the  ship  sails  as  when  it  is  at  rest.  And 
gnats  or  flies  can  as  easily  dance  among  one  another 
in  a  moving  cabin,  as  in  a  fixed  chamber.  As  for 
those  scripture-expressions  which  seem  to  contradict 
the  Earth's  motion,  the  following  reply  may  be  made 
to  them  all :  It  is  plain,  from  many  instances,  that 
the  Scriptures  were  never  intended  to  instruct  us  in 
philosophy  or  astronomy;  and  therefore,  on  those 
subjects,  expressions  are  not  always  to  be  taken  in 
the  literal  sense ;  but  for  the  most  part  as  accom- 
modated to  the  common  apprehensions  of  mankind. 
Men  of  sense  in  all  ages,  when  not  treating  of  the 
sciences  purposely,  have  followed  this  method: 
and  it  would  be  in  vain  to  follow  any  other  in  ad- 
dressing ourselves  to  the  vulgar,  or  bulk  of  any 


86  The  Phenomena  of  the  Heavens  as  seen 

community.  Moses  calls  the  Moon  a  GREAT 
LUMINARY  (as  it  is  in  the  Hebrew)  as  well  as 
the  Sun :  but  the  Moon  is  known  to  be  an  opaque 
body,  and  the  smallest  that  astronomers  have  observ- 
ed in  the  heavens ;  and  that  it  shines  upon  us,  not 
by  any  inherent  light  of  its  own,  but  by  reflecting 
the  light  of  the  Sun.  Moses  might  know  this ;  but 
had  he  told  the  Israelites  so,  they  would  have  stared  at 
him  ;  and  considered  him  rather  as  a  madman,  than 
as  a  person  commissioned  by  the  Almighty  to  be 
their  leader. 

CHAP.  IV. 

The  Phenomena  of  the  Heavens  as  seen  from  different 
Parts  of  the  Earth. 

We  are  "ITITTE  are  kept  to  the  Earth's  surface,  on 

Eea?A°bye  '  W    al1  sides,  by  the  power  of  its  central 

gravity,  attraction  ;  which  laying  hold  of  all  bodies  accord- 
ing to  their  densities  or  quantities  of  matter,  with- 
out regard  to  their  bulks,  constitutes  what  we  call 
their  weight.  And  having  the  sky  over  our  heads, 
go  where  we  will,  and  our  feet  toward  the  centre 
of  the  Earth ;  we  call  it  up  over  our  heads,  and 
down  under  our  feet :  although  the  same  right  line 
which  is  dozvn  to  us,  if  continued  through  and  be- 
yond the  opposite  side  of  the  Earth,  would  be  up  to 
Plate  //.  the  inhabitants  on  the  opposite  side.  For,  the  in- 
Flg* L  habitants  n,  z,  e,  m,  s,  0,  g,  /,  stand  with  their  feet 
toward  the  Earth's  centre  C;  and  have  the  same 
figure  of  sky  JV,  /,  E,  M,  S,  0,  Q,  Z,  over  their 
heads.  Therefore,  the  point  S  is  as  directly  upward 
to  the  inhabitant  s  on  the  south  pole,  as  N  is  to  the 
inhabitant  n  on  the  north  pole :  so  is  E  to  the 
inhabitant  e  supposed  to  be  on  the  north  end  of 
Peru  ;  and  Q  to  the  opposite  inhabitant  q  on  the  mid- 
A"*j-  die  of  the  island  Sumatra.  Each  of  these  observers 
is  surprised  that  his  opposite  or  antipode  can  stand 
with  his  head  hanging  downward-  But  let  eittejr 


from  different  Parts  of  the  Earth.  87 

go  to  the  other,  and  he  will  tell  him  that  he  stood  as  piate  //. 
upright  and  firm  on  the  place  where  he  was,  as  he 
now  stands  where  he  is.    To  all  these  observers,  the 
Sun,    Moon,    and,  stars,  seem    to  turn  round  the 
points  A"  and  S,  as  the  poles  of  the  fixed  axis  jVCS;  Axis  of 
because  the  Earth  does  really  turn  round  the  mathe-  th«  world. 

maticai  line  n  C  s  as  round  an  axis  of  which  n  is  the  T,      , 

i  rm     -II-         r  T  *ts  poles- 

north  pole,  and  s  the  south  pole.      1  he  inhabitant  u 

(Fig.  II.)  affirms  that  he  is  on  the  uppermost  side  of  Fig.  n. 
the  Earth,  and  wonders  how  another  at  L  can  stand  at 
the  undermost  side,  with  his  head  hanging  down- 
wards. But  Lf'm  the  mean  time  forgets,  that  in  twelve 
hours  time  he  will  be  carried  half  round  with  the 
Earth,  and  then  be  in  the  very  sit  nation  tliat  L  now 
is;  although  as  far  from  him  as  before^  a'ffd  yet,  when 
//comes  there,  he  will  find  no  difference  as  to  his 
manner  of  standing ;  only  he  will  see  the  opposite 
half  of  the  heavens,  and  imagine  the  heavens  to  have 
gone  half  round  the  Earth. 

123.  When  we  see  a  globe  hung  up  in  a  room,  How  our 
we  cannot  help  imagining  it  to  have  an  upper  and  an  Earth 
under  side,  and  immediately  form  a  like  idea  of  the  J^Je  L 
Earth ;  from  whence  we  conclude,  that  it  is  as  im-  upper 
possible  for  people  to  stand  on  the  under  side  of  the  ^"fle^n 
Earth,  as  for  pebbles  to  lie  on  the  under  side  of  a  side. 
common  globe,  which  instantly  fall  down  from  it  to 
the  ground;  and  well  they  may,  because  the  attraction 
of  the  Earth  being  greater  than  the  attraction  of  the 
globe,  pulls  them  away.     Just  so  would  it  be  with 
our  Earth,  if  it  were  fixed  near  a  globe  much  big- 
ger than  itself,  such  as  Jupiter:  for  then,  it  would 
really  have  an  upper  and  an  under  side  with  respect 
to  that  large  globe;  which,  by  its  attraction,  would 
pull  away  every  thing  from  the  side  of  the  Earth  next 
to  it ;  and  only  those  bodies  on  its  surface,  at  the  op- 
posite side,  could  remain  upon  it.    But  there  is  no 
larger  globe  near  enough  our  Earth  to  overcome  its 

M 


88  The  Phenomena  of  the  Heavens  as  seen 

Plate  II.  central  attraction ;  and  therefore  it  has  no  such  thing 
as  an  upper  and  an  under  side  ;  for  all  bodies  on  or 
near  its  surface,  even  to  the  Moon,  gravitate  toward 
its  centre. 

124.  Let  any  man  imagine  the  Earth,  and  every 
thing  but  himself,  to  be  taken  away,  and  he  left  alone 
in  the  midst  of  indefinite  space ;  he  could  then  have 
no  idea  of  up  or  clorun;  and  were  his  pockets  full  of 
gold,  he  might  tdke  the  pieces  one  by  one,  and  throw 
them  away  on  all  sides  of  him,  without  any  danger 
of  losing  them  ;  for  the  attraction  of  his  body  would 
bring  them  all  back  by  the  ways  they  went,  and  he 
would  be  down  to  every  one  of  them.  But  then,  if 
a  sun,  or  any  other  large  body,  were  created  and 
placed  in  any  part  of  space,  several  millions  of  miles 
from  him,  he  would  be  attracted  toward  it,  and  could 
not  save  himself  from  falling  down  to  it. 

*%•  I-  125.  The  Earth's  bulk  is  but  a  point,  as  that  at 

C,  compared  to  the  heavens ;  and  therefore  every 
inhabitant  upon  it,  let  him  be  where  he  will,  as  at 
?z,  £,  7?z,  s,  ckc.  sees  half  of  the  heavens.    The  inha- 
bitant >7,  on  the  north  pole  of  the  Earth,  constantly 
sees  the  hemisphere  E  N  Q;  and  having  the  north 
pole  A*  of  the  heavens  just  over  his  head,  his  hori. 
zon   coincides  with  the  celestial  equator  E  C  Q. 
Half  of     Therefore  all  the  stars  in  the  northern  hemisphere 
the  hea-    j?  jy>  Q  between  the  equator  and  north  pole,  appear 

vensvisi-  ,    ,       ,.         f»^» 

bietoan    f6  turn  round  the  line  JV  C,  moving  parallel  to  the 
inhabitant  horizon.     The  equatorial  stars  keep  in  the  horizon, 
partof the  anc^  a^  those  in  the  southern  hemisphere  E  S  Q  are 
Earth.      invisible.    The  like  phenomena  are  seen  by  the  ob- 
server s  on  the  south  pole,  with  respect  to  the  hemi- 
sphere E  S  Q;  and  to  him  the  opposite  hemisphere 
is  always  invisible.     Hence,  under  either  pole,  only 


from  different  Parts  of  the  Earth.  89 

one  half  of  the  heavens  is  seen;  for  those  parts  which 
are  once  visible  never  set,  and  those  which  are  once 
invisible  never  rise.  But  the  ecliptic  1'  C  X,  or  or- 
bit which  the  Sun  appears  to  describe  once  a  year 
by  the  Earth's  annual  motion,  has  the  half  Y  C  con- 
stantly above  the  horizon  E  C  Q  of  the  north  pole 
n;  and  the  other  half  C  X  always  below  it.  There-  Pheno- 
fore  while  the  Sun  describes  the  northern  half  Y  C!?ena  f 

..  .  .  .  the  poles. 

of  the  ecliptic,  he  neither  sets  to  tne  north  pole,  nor 
rises  to  the  south ;  and  while  he  describes  the  sou- 
thern half  C  X,  he  neither  sets  to  the  south  pole, 
nor  rises  to  the  north.  The  same  things  are  true 
with  respect  to  the  Moon;  only  with  this  difference, 
that  as  the  Sun  describes  the  ecliptic  but  once  a  year, 
he  is  for  half  that  time  visible  to  each  pole  in  its  turn, 
and  as  long  invisible;  but  as  the  Moon  goes  round 
the  ecliptic  in  27  days  8  hours,  she  is  only  visible  for 
13  days  16  hours,  and  as  long  invisible  to  each  pole 
by  turns.  All  the  planets  likewise  rise  and  set  to  the 
poles,  because  their  orbits  are  cut  obliquely  in  halves 
by  the  horizon  of  the  poles.  When  the  Sun  (in  his 
apparent  way  from  X)  arrives  at  C,  which  is  on  the 
20th  of  March,  he  is  just  rising  to  an  observer  at  n, 
on  the  north  pole,  and  setting  to  another  at  ,y,  on  the 
south  pole.  From  C  he  rises  higher  and  higher  in 
every  apparent  diurnal  revolution,  till  he  comes  to 
the  highest  point  of  the  ecliptic  y,  on  the  21st  of 
June;  when  he  is  at  his  greatest  altitude,  which  is 
23£  degrees,  or  the  arc  E  y,  equal  to  his  greatest 
north  declination ;  and  from  thence  he  seems  to  de- 
scend gradually  in  every  apparent  circumvolution, 
till  he  sets  at  C  on  the  23d  of  September;  and  then 
he  goes  to  exhibit  the  like  appearances  at  the  south 
pole  for  the  other  half  of  the  year.  Hence  the  Sun's 
apparent  motion  round  the  Earth  is  not  in  parallel 
circles,  but  in  spirals ;  such  as  might  be  represented 
by  a  thread  wound  round  a  globe  from  tropic  to  tro- 
pic ;  the  spirals  being  at  some  distance  from  one  an- 


90  The  Phenomena  of  the  Heavens  as  seen 

Plate  ii.   other  about  the  equator,  and  gradually  nearer  to  each 

other  as  they  approach  toward  the  tropics, 
pheno-  1^*  ^  tne  observer  be  any  where  on  the  terres- 
mena  at  trial  equator  e  C  q,  as  suppose  at  ?,  he  is  in  the  plane 
torCqUa"  °^  tne  ce^est^al  equator;  or  under  the  equinoctial 
E  C  Q;  and  the  axis  of  the  Earth  n  C  s  is  coinci- 
_.  .  dent  with  the  plane  of  his  horizon,  extended  out  to 
JVand  6*,  the  north  and  south  poles  of  the  heavens. 
As  the  Earth  turns  round  the  line  A*  C  S>  the  whole 
heavens  MOLL  seem  to  turn  round  the  same  line, 
but  the  contrary  way.  It  is  plain  that  this  observer 
has  the  celestial  poles  constantly  in  his  horizon,  and 
that  his  horizon  cuts  the  diurnal  paths  of  all  the  ce- 
lestial bodies  perpendicularly,  and  in  halves.  There- 
fore the  Sun,  planets,  and  stars,  rise  every  day,  as- 
cend perpendicularly  above  the  horizon  for  six  hours, 
and,  passing  over  the  meridian,  descend  in  the  same 
manner  for  the  six  following  hours  ;  then  set  in  the 
horizon,  and  continue  twelve  hours  below  it.  Con- 
sequently at  the  equator  the  days  and  nights  arc 
equally  long  throughout  the  year.  When  the  obser- 
ver is  in  the  situation  e>  he  sees  the  hemisphere 
S  E  A";  but  in  twelve  hours  after,  he  is  carried  half 
round  the  Earth's  axis  to  q,  and  then  the  hemisphere 
S  Q  A'  becomes  visible  to  him,  and  SE  N  disap- 
pears. Thus  we  find,  that  to  an  observer  at  either  of 
the  poles,  one  half  of  the  sky  is  always  visible,  and 
the  other  half  never  seen ;  but  to  an  observer  on  the 
equator  the  whole  sky  is  seen  every  24  hours. 

The  figure  here  referred  to,  represents  a  celes- 
tial globe  of  glass,  having  a  terrestrial  globe  within 
it :  after  the  manner  of  the  glass  sphere  invented  by 
my  generous  friend  Dr.  LONG,  JLtiWrides's  Profes- 
sor of  Astronomy  in  Cambridge. 

Remark.  127.  If  a  globe  be  held  side  wise  to  the  eye,  at 
some  distance,  and  so  that  neither  of  its  poles  can 
be  seen,  the  equator  E  C  Q,  and  all  circles  parallel 
to  it,  as  D  L,  y  z  x,  a  b  X,  MO,  &c.  will  appear  to  be 


from  different  Parts  of  the  Earth.  91 

straight  lines,  as  projected  in  this  figure ;  which  is 
requisite  to  be  mentioned  here,  because  we  shall 
have  occasion  to  call  them  circles  in  the  following 
articles  of  this  chapter*. 

128.  Let  us  now  suppose  that  the  observer  has^™^ 
gone  from  the  equator  €  toward  the  north  pole  7?,  tween  the 
and  that  he  stops  at  i,  from  which  place  he  thenequator 
sees  the  hemisphere  MEWL;  his  horizon  7IfCXandpo1 
having  shifted  as  many  degrees  from  the  celestial 
poles  A*  and  S,  as  he  has  travelled  from  under  the 
equinoctial  £.     And  as  the  heavens  seem  constantly 
to  turn  round  the  line  NCS  as  an  axis,  all  those  stars 
which  are  not  as  many  degrees  from  the  north  pole 
A"  as  the  observer  is  from  the  equinoctial,  namely, 
the  stars  north  of  the  dotted  parallel  DL,  never  set 
below  the  horizon  ;  and  those  which  are  south  of  the 
dotted  parallel  MO  never  rise  above  it.    Hence  the 
former  of  these  two  parallel  circles  is  called  the  cir-  The  cir- 
cle  of  perpetual  apparition,  and  the  latter  the  circle  ^^^ 
of  perpetual  occultation :  but  all  the  stars  between  apparition 
these  two  circles  rise  and  set  every  clay.    Let  us  im- andoccul- 

*  tation. 

agine  many  circles  to  be  drawn  between  these  two, 
and  parallel  to  them  ;  those  which  are  on  the  north 
side  of  the  equinoctial  will  be  unequally  cut  by  the 
horizon  MCL,  having  larger  portions  above  the  ho- 
rizon than  below  it :  and  the  more  so,  as  they  are 
nearer  to  the  circle  of  perpetual  apparition ;  but  the 
reverse  happens  to  those  on  the  south  side  of  the 
equinoctial  while  the  equinoctial  is  divid<  d  in  two 
equal  parts  by  the  horizon.  Hence,  by  the  apparent 
turning  of  the  heavens,  the  northern  stars  describe 
greater  arcs  or  portions  of  circles  above  the  horizon 
than  below  it ;  and  the  greater,  as  they  are  farther 
from  the  equinoctial  toward  the  circle  of  perpetual 
apparition ;  while  the  contrary  happens  to  all  stars 

*  The  plane  of  a  circle,  or  a  thin  circular  plate,  being  turned 
edge-wise  to  the  eye,  appears  to  be  a  straight  line. 


•1 

\f 
92  The  Phenomena  of  the  Heavens  as  seen 

south  of  the  equinoctial ;  but  those  upon  it  describe 
equal  arcs  both  above  and  below  the  horizon,  and 
therefore  they  are  just  as  long  above  it  as  below  it. 

129.  An  observer  on  the  equator  has  no  circle  of 
perpetual  apparition  or  occultation,  because  all  the 
stars,  together  with  the  Sun  and  Moon,  rise  and  set 
to  him  every  day.     But,  as  a  bare  view  of  the  fi- 
gure is  sufficient  to  shew  that  these  two  circles  DL 
and  MO  are  just  as  far  from  the  poles  A*  and  £as  the 
observer  at  i  (or  one  opposite  him  at  o,)  is  from  the 
equator  ECQ;  it  is  plain,  that  if  an  observer  begins 
to  travel  from  the  equator  to  ward  either  pole,  his  cir- 
cle of  perpetual  apparition  rises  from  that  pole  as 
from  a  point,  and  his  circle  of  perpetual  occultation 
from  the  other.     As  the  observer  advances  toward 
the  nearer  pole,  these  two  circles  enlarge  their  diame- 
ters, and  come  nearer  to  one  another,  until  he  comes 
to  the  pole ;  and  then  they  meet  and  coincide  in  the 
equinoctial.     On  different  sides  of  the  equator,  to 
observers  at  equal  distances  from  it,  the  circle  of  per- 
petual apparition  to  one  is  the  circle  of  perpetual  oc- 
cultation to  the  other. 

130,  Because  the  stars  never  vary  their  distances 
^rom  ^e  e(luinoc^alj  so.  as  to  be  sensible  in  an  age, 

scribe  the  the  lengths  of  their  diurnal  and  nocturnal  arcs  are  al- 
same  par-  ways  the  same  to  the  same  places  on  the  Earth.  But 
motion,  as  ^e  E-artn  goes  round  the  Sun  every  year  in  the 
and  the  ecliptic,  one  half  of  which  is  on  the  north  side  of 
tne  equinoctial,  and  the  other  half  on  its  south  side, 
the  Sun  appears  to  change  his  place  every  day ;  so 
as  to  go  once  round  the  circle  YCX  every  year, 
§  114.  Therefore  while  the  Sun  appears  to  advance 
northward,  from  having  described  the  parallel  a  b  X 
touching  the  ecliptic  in  Jf,  the  days  continually 
lengthen  and  the  nights  shorten,  until  he  comes  to  y, 
and  describes  the  parallel  yzx;  when  the  days  are 
at  the  Ipngest  and  the  nights  at  the  shortest:  for  then 


JVEf      ; 


from  different  Parts  of  the  Earth. 


us  the  Sun  goes  no  farther  northward,  the  greatest  Plate  IL 
portion  that  is  possible  of  the  diurnal  arc  y  z  is  above 
the  horizon  of  the  inhabitant  i;  and  the  smallest  por- 
tion z  x  below  it.  As  the  Sun  declines  southward 
from  z/,  he  describes  smaller  diurnal  and  greater  noc- 
turnal arcs  or  portions  of  circles  every  day  ;  which 
causes  the  days  to  shorten  and  the  nights  to  length- 
en, until  he  arrives  again  at  the  parallel  a  b  X;  which 
having  only  the  small  part  a  b  above  the  horizon 
MCL,  and  the  great  part  b  A"  below  it,  the  days 
are  at  the  shortest  and  the  nights  at  the  longest  :  be- 
cause the  Sun  recedes  no  farther  south,  but  returns 
northward  as  before.  It  is  easy  to  see  that  the  Sun 
must  be  in  the  equinoctial  E  C  Q  twice  every  year, 
and  then  the  days  and  nights  are  equally  long  ;  that 
is,  12  hours  each.  These  hints  serve  at  present  to 
give  an  idea  of  some  of  the  appearances  resulting 
from  the  motions  of  the  Earth  :  which  will  be  more 
particularly  described  in  the  tenth  chapter. 

131.  To  an  observer  at  either  pole,  the  horizon  pig-,  i. 
and  equinoctial  are  coincident  ;  and  the  Sun  and  stars  Parallel, 
seem  to  move  parallel  to  the  horizon  :  therefore  such  and^lg 
an  observer  is  said  to  have  a  parallel  position  of  the  spheres, 
sphere.     To  an  observer  any  where  between  either  what* 
pole  and  equator,  the  parallels  described  by  the  Sun 
and  stars  are  cut  obliquely  by  the  horizon,  and  there- 
fore he  is  said  to  have  an  oblique  position  of  the 
sphere.     To  an  observer  any  where  on  the  equator 
the  parallels  of  motion,  described  by  the  Sun  and 
stars,  are  cut  perpendicularly,  or  at  right  angles,  by 
the  horizon  ;  and  therefore  he  is  said  to  have  a  right 
position  of  the  sphere.     And  these  three  are  all  the 
different  ways  that  the  sphere  can  be  posited  to  the 
inhabitants  of  the  Earth. 


94  The  Phenomena  of  t/ie  Heavens  as  seen 


CHAP.  V. 

The  Phenomena  of  the  Heavens  as  seen  from  diffe- 
rent Parts  oj  the  Solar  System. 

132  C^  vastly  great  is  the  distance  of  the  starry 
"  I^J  heavens,  that  if  viewed  from  any  part  of 
the  solar  system,  or  even  many  millions  of  miles 
beyond  it,  the  appearance  would  be  the  very  same 
as  it  is  to  us.  The  Sun  and  stars  would  all  seem  to 
be  fixed  on  one  concave  suriace,  oi  which  the  spec- 
tator's eye  would  be  the  centre.  But  the  planets, 
being  much  nearer  than  the  stars,  their  appearances 
will  vary  considerably  with  the  place  from  which 
they  are  viewed. 

133.  If  the  spectator  be  at  rest  without  the  orbits 
of  the  planets,  they  will  seem  to  be  at  the  same  dis- 
tance as  the  stars;  but  continually  changing  their 
places  with  respect  to  the  stars,  and  to  one  another  ; 
assuming  various  phases  of  increase  and  decrease 
like  the  Moon  ;  and,  notwithstanding  their  regular 
motions  about  the  Sun,  will  sometimes  appear  to 
move  quicker,  sometimes  slower,  be  as  often  to  the 
west  as  to  the  east  of  the  Sun,  and  at  their  greatest 
distances  seem  quite  stationary.  The  duration,  ex- 
tent, and  distance,  of  those  points  in  the  heavens 
where  these  digressions  begin  and  end,  would  be 
more  or  less,  according  to  the  respective  distances 
of  the  several  planets  from  the  Sun  :  but  in  the  same 
planet,  they  would  continue  invariably  the  same  at 
all  times  ;  —  like  pendulums  of  unequal  lengths  oscil- 
lating together,  the  shorter  would  move  quick,  and  go 
over  a  small  space  ;  the  longer  would  move  slow,  and 
go  over  a  large  space.  If  the  observer  be  at  rest  with- 
in the  orbits  of  the  planets,  but  not  near  the  common 
centre,their  apparent  motions  will  be  irregular;  but  less 
so  than  in  the  former  case.  Each  of  the  several  planets 
will  appear  larger  and  less  by  turns,  as  they  approach 


from  different  Parts  of  the  Solar  System.  95 

nearer  to,  or  recede  farther  from,  the  observer;  the 
nearest  varying  most  in  their  size.  They  will  also 
move  quicker  or  slower  with  regard  to  the  fixed  stars, 
but  will  never  be  either  retrograde  or  stationary. 

134.  If  an  observer  in  motion  view  the  heavens, 
the  same  apparent  irregularities  will  be  observed, 
but  with  some  variation  resulting  from  his  own  mo- 
tion.    If  he  be  on  a  planet  which  has  a  rotation  on 
its  axis,  not  being  sensible  of  his  own  motion,  he 
will  imagine  the  whole  heavens,  Sun,  planets,  and 
stars,  to  revolve  about  him  in  the  same  time  that  his 
planet  turns  round,  but  the  contrary  way  ;  and  will 
not  be  easily  convinced  of  the  deception.  If  his  pla- 
net move  round  the  Sun,   the  same  irregularities 
and  aspects  as  above  mentioned  will  appear  in  the 
motions  of  the  other  planets  ;  and  the  Sun  will  seem 
to  move  among  the  fixed  stars  or  signs,  in  an  oppo- 
site direction  to  that  in  which  his  planet  moves, 
changing  its  place  every  day  as  he  does.     In  a  word, 
whether  our  observer  be  in  motion  or  at  rest,  whe- 
ther within  or  without  the  orbits  of  the  planets,  their 
motions  will  seem  irregular,  intricate,  and  perplex- 
ed, unless  he  be  placed  in  the  centre  of  the  system; 
and  from  thence,  the  most  beautiful  order  and  har- 
mony will  be  seen  by  him. 

135.  The  Sun  being  the  centre  of  all  the  planets'  The  Sun's 
motions,  the  only  place  from  which  their  motions 


could  be  truly  seen,  is  the  Sun's  centre  ;  where  the  from 
observer  being  supposed  not  to  turn  round  with  the  whlcl 


true  mo- 


Sllll  (which,  in  this  case,  we  must  imagine  to  be  ations  and 
transparent  body)  would  see  all  the  stars  at  rest,  gj*06^ 
and  seemingly  equidistant  from  him.     To  such  an  netsPcouid 
observer,  the  planets  would  appear  to  move  among  be  seen, 
the  fixed  stars ;  in  a  simple,  regular,  and  uniform 
manner :  only,  that  as  in  equal  times  they  describe 
equal  areas,  they  would  describe  spaces  somewhat 
unequal,  because  they  move  in  elliptic  orbits,  §  155. 
Their  motions  would  also  appear  to  be  what  they 
are  in  fact,  the  same  way  round  the  heavens ;  in 

N 


96  The  Phenomena  of  the  Heavens  as  seen 

paths  which  cross  at  small  angles  in  different  parts 
of  the  heavens,  and  then  separate  a  little  from  one 
another,  $  20.  So  that,  if  the  solar  astronomer 
should  make  the  path  or  orbit  of  any  planet  a  stand- 
ard, and  consider  it  as  having  no  obliquity,  §  201, 
he  would  judge  the  paths  of  ail  the  rest  to  be  inclined 
to  it ;  each  planet  having  one  half  of  its  path  on  one 
side,  and  the  other  half  on  the  opposite  side  of  the 
standard-path  or  orbit.  And  if  he  should  ever  see 
all  the  planets  start  from  a  eonj  unction  with  each 
other *,  Mercury  would  move  so  much  faster  than 
Venus,  as  to  overtake  her  again  (though  not  in  the 
same  point  of  the  heavens)  in  a  space  of  time  about 
equal  to  145  of  our  days  and  nights,  or,  as  we  com- 
monly call  them,  natural  days?  which  include  both 
the  days  and  nights :  Venus  would  move  so  much 
faster  than  the  Earth,  as  to  overtake  it  again  in  585 
natural  days :  the  Earth  so  much  faster  than  Mars, 
as  to  overtake  him  again  in  778  such  days :  Mars  so 
much  faster  than  Jupiter,  as  to  overtake  him  again 
in  817  such  days :  and  Jupiter  so  much  faster  than 
Saturn,  as  to  overtake  him  again  in  7236  days,  all 
of  our  time. 
Theju%-  13 gr  But  as  our  soiar  astronomer  could  have  no 

ment  that .  ,          P  .  .,    ,  , 

a  solar  as-  idea  of  measuring  the  courses  of  the  planets  by  our 
tronomer  days,  he  would  probably  take  the  period  of  Mer- 
probably  curv>  which  is  the  quickest-moving  planet,  for  a 
make  con-  measure  to  compare  the  periods  of  the  others  with. 
the^E  ^s  a^  ^e  stars  would  appear  quiescent  to  him,  he 
tances  and  would  never  think  that  they  had  any  dependance 
ma&ni-  upon  the  Sun;  but  would  naturally  imagine  that 

tildes  of  J  *    .  i 

the  pia-  the  planets  have,  because  they  move  round  the 
net*.  Sun.  And  it  is  by  no  means  improbable,  that  he 

*  Here  we  dp  Rot  mean  such  a  conjunction,  as  that  the  nearest 
planet  should  hide  all  the  rest  from  the  observer's  sight ;  (for  that 
would  be  impossible,  unless  the  intersections  of  all  their  orbits  were 
coincident,  which  they  are  not.  See  §  21.)  but  when  they  were  all 
in  a  line  crossing  the  standard-orbit  at  right  angles. 


from  different  Parts  of  the  Solar  System.  97 

would  conclude  those  planets,  whose  periods  are 
quickest,  to  move  in  orbits  proportionably  less  than 
those  do  which  make  slower  circuits.  But  being 
destitute  of  a  method  for  finding  their  parallaxes,  or, 
more  properly  speaking,  as  they  would  have  no  pa- 
rallax to  him,  he  could  never  know  any  thing  of 
their  real  distances  or  magnitudes.  Their  relative 
distances  he  might  perhaps  guess  at  by  their  periods, 
and  from  thence  infer  something  of  truth  concerning 
their  relative  magnitudes,  by  comparing  their  appa- 
rent magnitudes  with  one  another.  For  example, 
Jupiter  appearing  larger  to  him  than  Mars,  he  would 
conclude  it  to  be  so  in  fact ;  and  that  it  must  be  far- 
ther from  him,  on  account  of  its  longer  period* 
Mercury  and  the  Earth  would  appear  to  be  .nearly 
of  the  same  magnitude ;  but  .by  comparing  the  pe- 
riod of  Mercury  with  that  of  the  Earth,  he  would 
conclude  that  the  Earth  is  much  farther  from  him 
than  Mercury,,  and  consequently  that  it  must  be 
really  larger  though  apparently  of  the  same  magni- 
tude ;  and  so  of  the  rest.  And  as  each  planet  would 
appear  somewhat  larger  in  one  part  of  its  orbit  than 
in  the  opposite,  and  to  move  quickest  when  it  seems 
largest,  the  observer  would  be  at  no  loss  to  con- 
clude that  all  the  planets  move  in  orbits,  of  which 
the  Sun  is  not  precisely  the  centre. 

137.  The  apparent  magnitudes  of  the  planets  The  pia- 
continually  change  as  seen  from  the  Earth,  which  ^n^very" 
demonstrates  that  they  approach  nearer  to  it,  and  irregular 
recede  farther  from  it  by  turns.     From  these  phe-  ^^ 
nomena,   and  their   apparent   motions  among  the  Earth, 
stars,  they  seem  to  describe  loeped  curves,  which 
never  return  into  themselves,-*- Venus's  path  ex- 
cepted.     And  if  we  were  to  trace  out  all  their  ap- 
parent paths,  and  put  the  figures  of  them  together 
in  one  diagram,  they  would  appear  so  anomalous 
and  confused,  that  no  man  in  his  senses  could  be- 
lieve them  to  be  representations  of  their  real  paths ; 
but  would  immediately  conclude,  diat  such  appa- 


98  The  apparent  Paths  of  Mercury  and  Venus. 

Plate  ill.  rent  irregularities  must  be  owing  to  some  optic  illu- 
sions. And  after  a  good  deal  of  enquiry,  he  might 
perhaps  be  at  a  loss  to  find  out  the  true  causes  of 
these  irregularities;  especially  if  he  were  one  of 
those  who  would  rather,  with  the  greatest  justice, 
charge  frail  man  with  ignorance,  than  the  Almighty 
with  being  the  author  of  such  confusion. 
Mem  °f  ^  ^'  ^r*  ^°  N  G '  *n  kis  first  volume  of  Astronomy , 
and  Venus nas  giyen  us  figures  of  the  apparent  paths  of  all  the 
represent- planets,  separately  from  CASSINI;  and  on  seeing 
ed*  them  I  first  thought  of  attempting  to  trace  some  of 
them  by  a  machine*  that  shews  the  motions  of  the 
Sun,  Mercury,  and  Venus,  the  Earth,  and  Moon, 
according  to  the  Copernican  System.  Having  taken 
off*  the  Sun,  Mercury,  and  Venus,  I  put  black-lead 
pencils  in  their  places,  with  the  points  turned  up- 
ward ;  and  fixed  a  circular  sheet  of  paste- board  so, 
that  the  Earth  kept  constantly  under  its  centre  in 
going  round  the  Sun ;  and  the  paste-board  kept  its 
parallelism.  Then,  pressing  gently  with  one  hand 
upon  the  paste- board,  to  make  it  touch  the  three 
pencils;  with  the  other  hand  I  turned  the  winch  that 
moves  the  whole  machinery  :  and  as  the  Earth, 
together  with  the  pencils  in  the  places  of  Mercury 
Fte-L  and  Venus,  had  their  proper  motions  round  the 
Sun's  pencil,  which  kept  at  rest  in  the  centre  of 
the  machine,  all  the  three  pencils  described  a  dia- 
gram, from  which  the  first  figure  of  the  third  plate 
is  truly  copied  in  a  smaller  size.  As  the  Earth 
moved  round  the  Sun,  the  Sun's  pencil  described 
the  dotted  circle  of  months,  whilst  Mercury's  pen- 
cil drew  the  curve  with  the  greatest  number  of 
loops,  and  Venus's  that  with  the  fewest.  In  their 
inferior  conjunctions  they  come  as  much  nearer  to 
the  Earth,  or  within  the  circle  of  the  Sun's  appa- 
rent motion  round  the  heavens,  as  they  go  beyond 
it  in  their  superior  conjunctions.  On  each  side  of 
the  loops  they  appear  stationary  :  in  that  part  of 

*  The  ORRERY  fronting  the  Title-Page. 


The  apparent  Paths  of  Mercury  and  Venus. 

each  loop  next  the  Earth,  retrograde ;  and  in  all  the  &ate 
rest  of  their  paths,  direct. 

If  Cassini's  figures  of  the  paths  of  the  Sun,  Mer- 
cury, and  Venus,  were  put  together,  the  figure,  as 
above  traced  out,  would  be  exactly  like  them.  It 
represents  the  Sun's  apparent  motion  round  the  eclip- 
tic, which  is  the  same  every  year ;  Mercury's  rr.o- 
tion  for  seven  years;  and  Venus's  for  eight;  in  which 
time  Mercury's  path  makes  23  loops,  crossing  itself 
so  many  times,  and  Venus's  only  five.  In  eight 
years  Venus  falls  so  nearly  into  the  same  apparent 
path  again,  as  to  deviate  very  little  from  it  in  some 
ages ;  but  in  what  number  of  years  Mercury  and  the 
rest  of  the  planets  would  describe  the  same  visible 
paths  over  again,  I  cannot  at  present  determine. 
Having  finished  the  above  figure  of  the  paths  of 
Mercury  and  Venus,  I  put  the  ecliptic  round  them 
as  in  the  doctor's  book  ;  and  added  the  dotted  lines 
from  the  Earth  to  the  ecliptic,  for  shewing  Mercu- 
ry's apparent  or  geocentric  motion  therein  for  one 
year ;  in  which  time  his  path  makes  three  loops,  and 
goes  on  a  little  farther. — This  shews  that  he  has  three 
inferior,  and  as  many  superior  conjunctions  with  the 
Sun  in  that  time ;  and  also  that  he  is  six  times  sta- 
tionary, and  thrice  retrograde.  Let  us  now  trace 
his  motion  for  one  year  in  the  figure. 

Suppose  Mercury  to  be  setting  out  from  A  to- 
ward B  (between  the  Earth  and  left-hand  corner 
of  the  plate)  and  as  seen  from  the  Earth,  his  mo-  Fig.  i. 
tion  will  then  be  direct,  or  according  to  the  order  of 
the  signs.  But  when  he  comes  to  B,  he  appears 
to  stand  still  in  the  23d  degree  of  nj,  at  F,  as  shewn 
by  the  line  B  F.  While  he  goes  from  B  to  C,  the 
line  B  F,  supposed  to  move  with  him,  goes  back- 
ward from  F.  to  J2,  or  contrary  to  the  order  of 
signs :  and  when  he  is  at  C,  he  appears  stationary 
at  E;  having  gone  back  111  degrees.  Now,  sup- 
pose him  stationary  on  the  first  of  January  at  C,  on 
the  tenth  of  that  month  he  will  appear  in  the  heavens 


100  The  apparent  Paths  of  Mercury  and  Venus. 

as  at  20,  near  F ;  on  the  20th  he  will  be  seen  as  at 
G;  on  the  31st  at//;  on  the  iOth  of  February  at  F; 
on  the  20th  at  K;  and  on  the  28th  at  L ;  as  the 
•dotted  lines  shew,  which  are  drawn  through  every 
tenth  days'  motion  in  his  looped  path,  and  con- 
tinued to  the  ecliptic.  On  the  10th  of  March  he 
appears  at  M;  on  the  20th  at  A";  and  on  the  31st 
at  O.  On  the  tenth  of  April  he  appears  stationary 
at  P ;  on  the  20th  he  seems  to  have  gone  back 
again  to  O;  and  on  the  30th  he  appears  stationary  at 
Q,  having  gone  back  llf  degrees.  Thus  Mercury 
seems  to  go  forward  4  signs  11  degrees,  or  £31  de- 
grees ;  and  to  go  back  only  1 1  or  12  degrees,  at  a 
mean  rate.  From  the  30th  of  April  to  the  10th  of 
May,  he  seems  to  move  from  Q  to  R ;  and  on  the 
20th  he  is  seen  at  S,  going  forward  in  the  same 
manner  again,  according  to  the  order  of  letters ;  and 
backward  when  they  go  back ;  which  it  is  needless 
to  explain  any  farther,  as  the  reader  can  trace  him 
out  so  easily,  through  the  rest  of  the  year.  The 
same  appearances  happen  in  Venus 's  motion ;  but 
as  she  moves  slower  than  Mercury,  there  are  longer 
intervals  of  time  between  them. 

Having  already,  $  120,  given  some  account  of 
the  apparent  diurnal  motions  of  the  heavens  as  seen 
Irom  the  different  planets,  we  shall  not  trouble  the 
reader  any  more  with  that  subject. 

CHAP.  VI. 

TJie  Ptolemean  System  refuted.     The  Motions Mnd 
Phases  of  Mercury  and  Venus  explained. 

HE  Tychonic  System,  §  97,  being  suffi- 
ciently  refuted  in  the  109th  article,  we 
shall  say  nothing  more  about  it. 

140.  The  Ptolemean  System,  §  96,  which  asserts 
the  Earth  to  be  at  rest  in  the  centre  of  the  uni- 
verse, and  all  the  planets  with  the  Sun  and  stars 
to  move  round  it,  is  evidently  false  and  absurd. 


The  Phenomena  of  the  inferior  Planets.  101 

For  if  this  hypothesis  were  true,  Mercury  and  Ve- 
nus could  never  be  hid  behind  the  Sun,  as  their  or- 
bits are  included  within  the  Sun's ;  and  again,  these 
two  planets  would  always  move  direct,  and  be  as 
often  in  opposition  to  the  Sun  as  in  conjunction  with 
him.  But  the  contrary  of  all  this  is  true  :  for  they 
are  just  as  often  behind  the  Sun  as  before  him,  ap- 
pear as  often  to  move  backward  as  forward,  and  are 
so  far  from  being  seen  at  any  time  in  the  side  of  the 
heavens  opposite  to  the  Sun,  that  they  are  never  seen 
a  quarter  of  a  circle  in  the  heavens  distant  from  him. 

141.  These  two  plaftets,  when  viewed  at  different  Appear  - 
times  with  a  good  telescope,  appear  in  all  the  various  Mercury- 
shapes  of  the  Moon  j  which  is  a  plain  proof  that  they  and  Ve~ 
are  enlightened  by  the  Sun,  and  shine  not  by  any nus* 
light  of  their  own ;  for  if  they  did,  they  would  con- 
stantly appear  round  as  the  Sun  does ;  and  could 
never  be  seen  like  dark  spots  upon  the  Sun  when 
they  pass  directly  between  him  and  us.     Their  re- 
gular phases  demonstrate  them  to  be  spherical  bo- 
dies; as  may  be  shewn  by  the  following  experiment : 

Hang  an  ivory  ball  by  a  thread,  and  let  any  per-  Experi- 
son  move  it  round  the  flame  of  a  candle,  at  two  or  ^e  [hey 
three  yards  distance  from  your  eye ;  when  the  ball  are  round., 
is  beyond  the  candle,  so  as  to  be  almost  hid  by  the 
flame,  its  enlightened  side  will  be  toward  you,  and 
appear  round  like  the  full  Moon :  When  the  ball 
is  between  you  and  the  candle,  its  enlightened  side 
will  disappear  as  the  Moon  does  at  the  change : 
When  it  is  half-way  between  these  two  positions,  it 
will  appear  half  illuminated,  like  the  Moon  in  her 
quarters :  but  in  every  other  place  between  these 
positions,  it  will  appear  more  or  less  horned  or  gib- 
bous.    If  this  experiment  be  made  with  a  flat  cir- 
cular plate,  you  may  make  it  appear  fully  enlight- 
ened, or  not  enlightened  at  all ;  but  can  never  mak/ 
it  appear  either  horned  or  gibbous. 


102  The  Phenomena  of  the  inferior  Planets. 

Plate  n.        142.  If  you  remove  about  six  or  seven  yards  from 
Experi-     the  candle,  and  place  yourself  so  that  its  flame  may 
represent  ^e  Just  at>out  the  height  of  your  eye,  and  then  de- 
the  mo-    sire  the  other  person  to  move  the  ball  slowly  round 
MercuL  ^ie  canc^le  as  before,  keeping  it  as  nearly  of  an  equal 
and  Ve-    height  with  the  flame  as  he  possibly  can,  the  ball 
nus-         will  appear  to  you  not  to  move  in  a  circle,  but  to  vi- 
brate backward  and  forward  like  a  pendulum ;  mov- 
ing quickest  when  it  is  directly  between  you  and  the 
candle,  and  when  directly  beyond  it ;  and  gradually 
slower  as  it  goes  farther  to  the  right  or  left  side  of 
the  flame,  until  it  appears  at  the  greatest  distance 
from  the  flame ;  and  then,  though  it  continues  to 
move  with  the  same  velocity,  it  will  seem  for  a  mo- 
ment to  stand  still.    In  every  revolution  it  will  shew 
all  the  above  phases,  §   141 ;  and  if  two  balls,  a 
smaller  and  a  greater,  be  moved  in  this  manner  round 
the  candle,  the  smaller  ball  beng  kept  nearest  the 
flame,  and  carried  round  almost  three  times  as  often 
as  the  greater,  you  will  have  a  tolerable  good  repre- 
sentation of  the  apparent  motions  of  Mercury  and 
Venus ;  especially  if  the  greater  ball  describe  a  cir- 
cle almost  twice  as  large  in  diameter  as  that  describ- 
ed by  the  lesser. 

FiS-  "I-        143.  Let  A  B  C  D  E  be  a  part  or  segment  of  the 
visible  heavens,  in  which  the  Sun,  Moon,  planets, 
and  stars,  appear  to  move  at  the  same  distance  from 
the  Earth  E.     For  there  are  certain  limits,  beyond 
which  the  eye  cannot  judge  of  different  distances; 
as  is  plain  from  the  Moon's  appearing  to  be  as  far 
from   us  as  the  Sun  and  stars  are.     Let  the  cir- 
cle fg  h  ik  Im  n  o  be  the  orbit  in  which  Mercury  m 
moves  round  the  Sun  S,   according  to  the  order 
of  the  letters.     When  Mercury  is  at/^  he  disap- 
pears to  the  Earth  at  E,  because  his  enlightened 
The  elon-  side  is  turned  from  it ;  unless  he  be  then  in  one  of 
dtgrTs8.  °r  his  nodes,  $  20,  25;  in  which  case  he  will  appear 
sions  of    like  a  dark  spot  upon  the  Sun.     When  he  is  at  g 
froTthl  m  his  orbit,  he  appears  at  B  in  the  heavens,  west- 

Sun. 


The  Phenomena  of  the  inferior  Planets.  103 

ward  of  the  Sun  S,  which  is  seen  at  C:  when  at  A,  Plate  n. 
he  appears  at  A,  at  his  greatest  western  elongation 
or  distance  from  the  Sun ;  and  then  seems  to  stand 
still.     But,  as  he  moves  from  h  to  i,  he  appears  to 
go  from  A  to  B  ;  and  seems  to  be  in  the  same  place 
when  at  i,  as  when  he  was  at  g,  but  not  near  so 
large  :  at  k  he  is  hid  from  the  Earth  E,  by  the  Sun 
6';  being  then  in  his  superior  conjunction.     In  go- 
ing from  k  to  /,  he  appears  to  move  from  C  to  D ; 
and  when  he  is  at  ;z,  he  appears  stationary  at  E ; 
being  seen  as  far  east  from  the  Sun  then,  as  he  was 
west  from  it  at  A.     In  going  from  n  to  0,  in  his 
orbit,  he  seems  to  go  back  again  in  the  heavens, 
from  E  to  D ;  and  is  seen  in  the  same  place  (with 
respect  to  the  Sun)  at  0,  as  when  he  was  at  /;  but 
of  a  larger  diameter  at  0,  because  he  is  then  nearer 
the  Earth  E :  and  when  he  comes  to  f,  he  again 
passes  by  the  Sun,  and  disappears  as  before.   In  go- 
ing from  n  to  A,  in  his  orbit,  he  seems  to  go  back- 
ward in  the  heavens  from  E  to  A;  and  in  going 
from  h  to  72,  he  seems  to  go  forward  from  A  to  E  : 
as  he  goes  on  from  f,  a  little  of  his  enlightened  side 
at  g  is  seen  from  E ;  at  h  he  appears  half  full,   be- 
cause half  of  his  enlightened   side   is  seen ;    at  iy 
gibbous,  or  more  than  half  full ;  and  at  k  he  would 
appear  quite  full,  were  he  not  hid  from  the  Earth 
E  by  the  Sun  S.     At  /  he  appears  gibbous  again,  at 
n  half  decreased,  at  o  horned,  and  at  f  new,  like  the 
Moon  at  her  change.     He  goes  sooner  from  his 
eastern  station  at  n  to  his  western  station  at  A,  than 
again  from  h  to  n ;  because  he  goes  through  less 
than  half  his  orbit  in  the  former  case,  and  through 
more  in  the  latter. 

144.  In  the  same  figure,  let  FGHIKLMN  be  Fig.  in. 
the  orbit  in  which  Venus  v  goes  round  the  Sun  S, 
according  to  the  order  of  the  letters :  and  let  E  be 
the  Earth,  as  before.     When  Venus  is  at  F,  she  is  The  eion- 
in  her  inferior  conjunction  ;  and  disappears  like  ^ef^ionhsa 
new  Moon,  because  her  dark  side  is  toward  theses  of  * 
Earth.     At  (r,  she  appears  half  enlightened  to  thev«nus- 

O 


104  The  Phenomena  of  the  inferior  Planets. 

Earth,  like  the  moon  in  her  first  quarter :  at  H9  she 

appears  gibbous ;  at  /,  almost  full ;  her  enlightened 

side  being  then  nearly  towards  the  Earth  ;  at  K,  she 

would  appear  quite  full  to  the  Earth  E ;  but  is  hid 

from  it  by  the  Sun  S ;  at  Z/,  she  appears  upon  the 

decrease,  or  gibbous ;  at  M,  more  so  ;  at  N,  only  half 

The  great-  enlightened ;  and  at  F,  she  again  disappears.  In  mov- 

est  eion-    ins,  from  jy  to  Q  sjle  seems  to  £o  backward  in  the 

gallons  01,°  ir-/^f          -\i»  11  11 

Mercury   heavens  ;  and  from  Cr  to  N9  forward  ;  but  as  she  de- 

and  Ve-    scribes  a  much  greater  portion  of  her  orbit  in  going 

from  G  to  A",  than  from  JVto  6r,  she  appears  much 

longer  direct  than  retrograde  in  her  motion.     At  A* 

and  G  she  appears  stationary  ;  as  Mercury  does  at 

n  and  /z.     Mercury,  when  stationary,  seems  to  be 

only  28  degrees  from  the  Sun ;   and  Venus,  when 

so,  47 ;  wh'ch  is  a  demonstration  that  Mercury's 

•orbit  is  included  within  Venus's,  and  Venus's  within 

the  Earth's. 

145.  Venus,  from  her  superior  conjunction  at  K> 
to  her  inferior  conjunction  at  F,  is  seen  on  the  east 
side  of  the  Sun  S,  from  the  Earth  E;  and  therefore 
she  shines  in  the  evening  after  the  Sun  sets,  and  is 

Morning   called  the  evening  star ;  for,  the  Sun  being  then  to 
and  even-  the  westward  of  Venus,  must  set  first.     From  her 
v?hattar*    *nfer*°r  conjunction  to  her  superior,  she  appears  on 
the  west  side  of  the  Sun  ;  and  therefore  rises  before 
him  ;  for  which  reason  she  is  called  the  nwrmng  star. 
When  she  is  about  A"  or  Gr,  she  shines  so  bright, 
that  bodies  by  her  light  cast  shadows  in  the  night- 
time. 

146.  If  the  Earth  kept  always  at  E,  it  is  evident 
that  the  stationary  places  of  Mercury  and  Venus 
would  always  be  in  the  same  points  of  the  heavens 
where   they   were    before*     For  example :    whilst 
Mercury  m  goes  from  h  to  77,  according  to  the  order 

f  he  sta-  of  the  letters,  he  appears  to  describe  the  arc  ABCDE 
tionary  jn  the  heavens,  direct :  and  while  he  goes  from  n  to 
fheCpia?  h>  ^ie  seems  to  describe  the  same  arc  back  again, 
netsvari-  from  E  to  Ay  retrograde j  always  at  n  and  n  he 

able. 


The  Phenomena  of  the  inferior  Planets*  105 

appears  stationary  at  the  same  points  E  and  A  as 
before.  But  Mercury  goes  round  his  orbit,  from/* 
to  f  again,  in  88  days;  and  yet  there  are  116  days 
from  any  one  of  his  conjunctions,  or  apparent  sta- 
tions, to  the  same  again :  and  the  places  of  these  con- 
junctions and  stations  are  found  to  be  about  114  de- 
grees eastward  from  the  points  of  the  heavens  where 
they  were  last  before ;  which  proves  that  the  Earth 
has  not  kept  all  that  time  at  E.,  but  has  bad  a  pro- 
gressive motion  in  its  orbit  from  E  to  /.  Venus  also 
differs  every  time  in  the  places  of  her  conjunctions 
and  stations ;  but  much  more  than  Mercury ;  be- 
cause, as  Venus  describes  a  much  larger  orbit  than 
Mercury  does,  the  Earth  advances  so  much  the  far- 
ther  in  its  annual  path,  before  Venus  comes  round 
again. 

147.  As  Mercury  and  Venus,    seen  from   theTheelon- 
Earth,  have  their  respective  elongations  from  the  f^g™  of 
Sun,  and  stationary  places ;  so  has  the  Earth,  seen  turn's  in. 
from   Mars;   and   Mars,   seen  from  Jupiter;   and ferior  Pla' 
Jupiter,  seen  from  Saturn  :  that  is,  to  every  supe-  seen  from 
rior  planet,  all  the  inferior  ones  have  their  stations  him- 
and  elongations;  as  Venus  and  Mercury  have  to 

the  Earth.  As  seen  from  Saturn,  Mercury  never 
goes  more  than  2^  degrees  from  the  Sun ;  Venus 
4*;  the  Earth  6;  Mars  9|;  and  Jupiter  33i ;  so  that 
Mercury,  as  seen  from  the  Earth,  has  almost  as 

freat  a  digression  or  elongation  from  the  Sun,  as 
upiter,  seen  from  Saturn. 

148.  Because  the  Earth's  orbit  is  included  with- A  proof  of 
in  the  orbits  of  Mars,  Jupiter,  and  Saturn,  they  are  ^en^[th's 
seen  on  all  sides  of  the  heavens  :  and  are  as  often  in  motion. 
opposition  to  the  Sun  as  in  conjunction  with  him. 

If  the  Earth  stood  still,  they  would  always  appear 
direct  in  their  motions ;  never  retrograde  nor  station- 
ary. But  they  seem  to  go  just  as  often  backward 
as  forward ;  which,  if  gravity  be  allowed  to  exist, 
affords  a  sufficient  proof  of  the  Earth's  annual  mo- 
tion :  and  without  its  existence,  the  planets  could 
never  fall  from  the  tangents  of  their  orbits  towards 


106  The  Phenomena  of  the  inferior  Planets. 

Plate  II.    the  Sun,  nor  could  a  stone,  which  is  once  thrown 
up  from  the  Earth,  ever  fall  to  the  earth  again. 

149.  As  Venus  and  the  Earth  are  superior  pla- 
nets to  Mercury,  they  exhibit  much  the  same  ap- 
pearances to  him,  that  Mars  and  Jupiter  do  to  us. 
Let  Mercury  m  be  at/;  Venus  v  at  F,  and  the  Earth 
p.    In     at  E;   in  which  situation  Venus  hides  the  Earth 
General*    from  Mercury ;  but  being  in  opposition  to  the  Sun, 
phenome-  sne  shines  on  Mercury  with  a  full  illumined  orb ; 
periorVia-  though,  with  respect  to  the  Earth,  she  is  in  con- 
net  to  an  junction  with  the  Sun,  and  invisible.     When  Mer- 
mfenor.    cury  jg  at  y-  an(j  yenus  at  £,  her  enlightened  side 

not  being  directly  toward  him,  she  appears  a  little 
gibbous ;  as  Mars  does  in  a  like  situation  to  us :  but, 
when  Venus  is  at  /,  her  enlightened  side  is  so  much 
toward  Mercury  at/J  that  she  appears  to  him  almost 
of  a  round  figure.  At  K,  Venus  disappears  to  Mer- 
cury at/J  being  then  hid  by  the  Sun ,  as  all  our  su- 
perior planets  are  to  us,  when  in  conjunction  with 
the  Sun.  When  Venus  has,  as  it  were,  emerged 
out  of  the  Sun-beams,  as  at  L,  she  appears  almost 
full  to  Mercury  at/;  at  M  and  A",  a  little  gibbous; 
quite  full  at  F,  and  largest  of  all ;  being  then  in  op- 
position to  the  Sun,  and  consequently  nearest  to 
Mercury  at  F;  shining  strongly  on  him  in  the  night, 
because  her  distance  from  him  then  is  somewhat  less 
than  a  fifth  part  of  her  distance  from  the  Earth,  when 
she  appears  roundest  to  it  between  /  and  K,  or  be- 
tween JSf  and  Z,,  as  seen  from  the  Earth  E.  Con- 
sequently, when  Venus  is  opposite  to  the  Sun  as 
seen  from  Mercury,  she  appears  more  than  25  times 
as  large  to  him  as  she  does  to  us  when  at  the  fullest. 
Our  case  is  almost  similar  with  respect  to  Mars, 
when  he  is  opposite  to  the  Sun ;  because  he  is  then 
so  near  the  Earth,  and  has  his  whole  enlightened 
side  toward  it.  But,  because  the  orbits  of  Jupiter 
and  S-iturn  are  very  large  in  proportion  to  the  Earth's 
orbit,  these  two  planets  appear  much  less  magnified 


The  Physical  Causes  of  the  Planets"  Motions.  107 


at  their   oppositions,  or  diminished  at  their 
junctions,  than  Mars  does,  in  proportion  to  their 
mean  apparent  diameters. 

CHAP.  VII. 

The  Physical  Causes  of  the  Motions  of  the  Planets. 
The  Eccentricities  of  their  Orbits.  The  Times  in 
which  the  Action  of  Gravity  'would  bring  them  to 
the  Sun.  ARCHIMEDES'S  ideal  Problem  for 
moving  the  Earth.  Tlie  World  not  eternal. 


ROM  the  uniform  projectile  motion 
bodies  in  straight  lines,  and  the  universal 
power  of  attraction  which  draws  them  off  from  these  tion. 
lines,  the  curvilineal  motions  of  all  the  planets  arise,  pig.  iv. 
If  the  body  A  be  projected  along  the  right  line  ABXy 
in  open  space,  where  it  meets  with  no  resistance, 
and  is  not  drawn  aside  by  any  other  power,  it  would 
for  ever  go  on  with  the  same  velocity,  and  in  the 
same  direction.  For,  the  force  which  moves  it 
from  A  to  B  in  any  given  time,  will  carry  it  from  B  circular 
to  Jf  in  as  much  more  time,  and  so  on,  there  being  orbits- 
nothing  to  obstruct  or  alter  its  motion.  But  if,  when 
this  projectile  force  has  carried  it,  suppose  to  Y?,  the 
body  S  begin  to  attract  it,  with  a  power  duly  adjust- 
ed, and  perpendicular  to  its  motion  atY?,  it  will  then 
be  drawn  from  the  straight  line  ABX,  and  forced  to 
revolve  about  S  in  the  circle  BYTU.  When  the  Fi^.  iv. 
body  A  comes  to  U,  or  any  other  part  of  its  orbit,  if 
the  small  body  z/,  within  the  sphere  of  IPs  attraction, 
be  projected,  as  in  the  right  line  Z,  with  a  force  per- 
pendicular to  the  attraction  of  Z7,  then  u  will  go 
round  £7  in  the  orbit  W,  and  accompany  it  in  its 
whole  course  round  the  body  S.  Here  S  may  re- 
present the  Sun,  £7  the  Earth,  and  u  the  Moon. 

151.  If  a  planet  at  B  gravitate,  or  be  attracted, 
toward  the  Sun,  so  as  to  fall  from  B  to  y  in  the 


108  The  Physical  Causes  of 

time  that  the  projectile  force  would  have  carried  it 
from  B  to  X,  it  will  describe  the  curve  B  Y  by  the 
combined  action  of  these  two  forces,  in  the  same 
time  that  the  projectile  force  singly  would  have  car- 
ried  it  from  B  to  X,  or  the  gravitating  power  singly 
have  caused  it  to  descend  from  B  to  y ;  and  these 
two  forces  being  duly  proportioned,  and  perpendi- 
cular to  each  other,  the  planet,  obeying  them  both, 
will  move  in  the  circle  BYTU*. 

152.  But  if,  while  the  projectile  force  would  carry 
the  planet  from  B  to  A,  the  Sun's  attraction  (which 
constitutes  the  planet's  gravitation)  should  bring  it 
down  from  B  to  1,  the  gravitating  power  would  then 
be  too  strong  for  the  projectile  force ;  and  would 
cause  the  planet  to  describe  the  curve  B  C.    When 
Elliptical  the  planet  comes  to  C,  the  gravitating  power  (which 
«rbits.      always  increases  as  the  square  of  the  distance  from 
the  Sun  S  diminishes)  will  be  yet  stronger  on  ac- 
count of  the  projectile  force  ;  and  by  conspiring  in 
some  degree  therewith,  will  accelerate  the  planet's 
motion  all  the  way  from  C  to  K ;  causing  it  to  de- 
scribe the  arcs  BC,  CD,  DE,  EF,  &c.  all  in  equal 
times.    Having  its  motion  thus  accelerated,  it  there- 
by gains  so  much  centrifugal  force  or  tendency  to 
fly  off  at  Km  the  line  JO*,  as  overcomes  the  Sun's 
attraction :  and  the  centrifugal  force  being  too  great 
to  allow  the  planet  to  be  brought  nearer  the  Sun,  or 
even  to  move  round  him  in  the  circle  Klmn,  &c.  it 
goes  off,  and  ascends  in  the  curve  KLMN,  &c.  its 
motion  decreasing  as  gradually  from  K  to  B,  as  it 
increases  from  B  to  K;  because  the  Sun's  attraction 
now  acts  against  the  planet's  projectile  motion  just 
as  much  as  it  acted  with  it  before.     When  the  pla- 
net has  got  round  to  J5,  its  projectile  force  is  as 
much  diminished  from  its  mean  state  about  G  or  A*, 

*  To  make  the  projectile  force  talance  the  gravitating  power  sc 
exactly  as  that  the  body  may  move  in  a  circle,  '.he  projectile  velocity 
of  the  "body  must  be  such  as  it  would  have  acquired  by  gravity  alone, 
in  falling  through  half  the  radius  of  the  circle. 


the  Planets'  Motion. 

as  it  was  augmented  at  K ' ;  and  so,  the  Sun's  attrac-  Plate  IL 
tion  being  more  than  sufficient  to  keep  the  planet 
from  going  off  at  B,  it  describes  the  same  orbit  over 
again,  by  virtue  of  the  same  forces  or  powers. 

153.  A  double  projectile  force  will  always  balance 
a  quadruple  power  of  gravity.     Let  the  planet  at  B 
have  twice  as  great  an  impulse  from  thence  toward 
Jf,  as  it  had  before ;  that  is,  in  the  same  length  of 
time  that  it  was  projected  from  B  to  6,  as  in  the  last 
example,  let  it  now  be  projected  from  B  to  c ;  and  it 
will  require  four  times  as  much  gravity  to  retain  it  in 
its  orbit :  that  is,  it  must  fall  as  far  as  from  B  to  4  in 
the  time  that  the  projectile  force  would  carry  it  from 
£  to  c;  otherwise  it  could  not  describe  the  curve 
BD  ;  as  is  evident  by  the  figure.     But,  in  as  much 

time  as  the  planet  moves  from  B  to  C  in  the  higher  Fig.  iy. 
part  of  its  orbit,  it  moves  from  /to  K,  or  from  Jfto  ™e  P**- 
L,  in  the  lower  part  thereof;  because,  from  the  joint  scriVe^ 
action  of  these  two  forces,  it  must  always  describe  equal  are- 
equal  areas  in  equal  times,  throughout  its  annual  Jfmes.q 
course.   These  areas  are  represented  by  the  triangles 
BSC,  CSDy  DSE,  ESF,  &c.  whose  contents' are 
equal  to  one  another  quite  round  the  figure. 

154.  As  the  planets  approach  nearer  the  Sun,  and  A  difficui- 
recede  farther  from  him,  in  every  revolution  ;  there  *y remov- 
may  be  some  difficulty  in  conceiving  the  reason  why 

the  power  of  gravity,  when  it  once  gets  the  better  of 
the  projectile  force,  does  not  bring  the  planets  nearer 
and  nearer  the  Sun  in  every  revolution,  till  they  fall 
upon,  and  unite  with  him ;  or  why  the  projectile  force, 
when  it  once  gets  the  better  of  gravity,  does  not 
carry  the  planets  farther  and  farther  from  the  Sun, 
till  it  removes  them  quite  out  of  the  sphere  of  his 
attraction,  and  causes  them  to  go  on  in  straight  lines 
for  ever  afterward.'  But  by  considering  the  effects 
of  these  powers  as  described  in  the  two  last  articles, 
this  difficulty  will  be  removed.  Suppose  a  planet 


1 10  The  Physical  Causes  of 

at  B,  to  be  carried  by  the  projectile  force  as  far  a$ 
from  B  to  £,  in  the  time  that  gravity  would  have 
brought  it  down  from  B  to  1 :  by  these  two  forces 
it  will  describe  the  curve  B  C.  When  the  planet 
comes  down  to  K,  it  will  be  but  half  as  far  from  the 
Sun  A$*as  it  was  at  B ;  and  therefore  by  gravitating 
four  times  as  strongly  towards  him,  it  would  fall 
from  K  to  V  in  the  same  length  of  time  that  it  would 
have  fallen  from  B  to  1  in  the  higher  part  of  its  or- 
bit; that  is  through  four  rimes  as  much  space  ;  but 
its  projectile  force  is  then  so  much  increased  at  Jf, 
as  would  carry  it  from  JTto  k  in  the  same  time; 
being  double  of  what  it  was  at  B ;  and  is  therefore 
too  strong  for  the  gravitating  power,  either  to  draw 
the  planet  to  the  Sun,  or  cause  it  to  go  round  him  in 
the  circle  Klmn,  &c.  which  would  require  its  falling 
from  K  to  w,  through  a  greater  space  than  that 
through  which  gravity  can  draw  it,  while  the  pro- 
jectile force  is  such  as  would  carry  it  from  A"  to  k : 
and  therefore  the  planet  ascends  in  its  orbit  KLMN; 
decreasing  in  its  velocity,  for  the  causes  already  as- 
signed in  §  152. 

The  pia-        155.  The  orbits  of  all  the  planets  are  ellipses,  very 

netary  or-  little  different  from  circles :   but  the  orbits  of  the 

tical?  lp    comets  are  very  long  ellipses ;  and  the  lower  focus 

of  them  all  is  in  the  Sun.     If  we  suppose  the  mean 

distance  (or  middle  between  the  greatest  and  least) 

of  every  planet  and  comet  from  the  Sun  to  be  divid- 

Their  ec-  ed  into  1000  equal  parts,  the  eccentricities  of  their 

centricU    orbits,  both  in  such  parts  and  in  English  miles,  will 

be  as  follow:  Mercury's,  210  parts,  or  6,720,000 

miles;    Venus's,    7  parts,  or  413,000  pniles;   the 

Earth's,  17  parts,  or  1,377,000  miles;  Mars's,  93 

pans,  or  11,439,000  miles;   Jupiter's,  48  parts,  or 

20,352,000  miles ;   Saturn's,  55  parts,  or  42,755, 

000   miles.     Of  the  nearest  of  the  tree  foremen- 

tioned  comets,  1,458,000  miles;  of  the  middlemost, 

2,025  000,000  miles;  and  of  the  outermost,  6,600, 

000,000. 


the  Planets'1  Motions.  1 1 1 

156.  By  the  above-mentioned  law,   J  150  &  seq.  The  above 
bodies  will  move  in  all  kinds  of  ellipses,  whether  Ions;  ]*ws  !.uffi' 

.  P    ,  Ai  .      ,  .  ,  .    °  cient  for 

or  short,  if  the  spaces  they  move  in  be  void  of  resist-  motions 
ance.     Only  those  which  move  in  the  longer  ellipses  b?th  in 
have  so  much  the  less  projectile  force  impressed  upon  ami  einV 
them  in  the  higher  parts  of  their  orbits  ;  and  their  ve-  tic  orbits. 
locities,  in  coming  down  towards  the  Sun,  are  so  pro- 
digiously increased  by  his  attraction,  that  their  centri- 
fugal forces  in  the  lower  parts  of  their  orbits  are  so 
great,  as  to  overcome  the  Sun's  attraction  there,  and 
cause  them  to  ascend  again  towards  the  higher  parts 
qf  their  orbit ;  during  which  time  the  Sun's  attraction, 
acting  so  contrary  to  the  motions  of  those  bodies, 
causes  them  to  move  slower  and  slower,  until  their 
projectile  forces  are  diminished  almost  to  nothing ; 
and  then  they  are  brought  back  again  by  the  Sun's 
attraction  as  before. 

157.  If  the  projectile  forces  of  all  the  planets  and  in  what 
comets  were  destroyed  at  their  mean  distances  from times  thc 
the  Sun,  their  gravities  would  bring  them  down  so,  wouid*faH 
as  that  Mercury  would  fall  to  the  Sun  in  15  days  13  totheSun 
hours;   Venus,  in  39  days  17  hours;   the  Earth  orbo4hrof 
Moon,  in  64  days  10  hours;  Mars,  in  121  days  ;  Ju-  gravity, 
piter,  in  290;  and  Saturn,  in   767.     The  nearest 
comet,  in  13  thousand  days;  the  middlemost,  in  23 
thousand  days ;  and  the  outermost,  in  66  thousand 

days.  The  Moon  would  fall  to  the  Earth  in  4  days 
20  hours ;  Jupiter's  first  moon  would  fall  to  him  in  7 
hours,  his  second  in  15,  his  third  in  30,  and  his  fourth 
in  71  hours.  Saturn's  first  moon  would  fall  to  him 
in  8  hours,  his  second  in  12,  his  third  in  19,  his 
fourth  in  68,  and  his  fifth  in  336  hours.  A  stone 
would  fall  to  the  Earth's  centre,  if  there  were  a  hollow 
passage,  in  21  minutes  9  seconds.  Mr.  WHISTON 
gives  the  following  rule  for  such  computations.  "  *It 
is  demonstrable,  'that  half  the  period  of  any  planet, 
when  it  is  diminished  in  the  sesquialteral  proportion 

*  Astronomical  Principles  of  Religion,  p.  66. 


112  The  Physical  Causes  of 

of  the  number  1  to  the  number  2,  or  nearly  in  the 
proportion  of  1000  to  2828,  is  the  time  in  which  it 
would  fall  to  the  centre  of  its  orbit. 

The  pro-        158.  The  quick  motions  of  the  moons  of  Jupiter 
dlgl°usna*fand  Saturn  round  their  primaries,  demonstrate  that 
ibeCSun°  these  two  planets  have  stronger  attractive  powers 
and  Pia-    than  the  Earth  has.     For  the  stronger  that  one  body 
nets*         attracts  another,  the  greater  must  be  the  projectile 
force,  and  consequently  the  quicker  must  be  the  mo- 
tion of  that  other  body  to  keep  it  from  falling  to  its 
primary  or  central  planet.     Jupiter's  second  moon  is 
124  thousand  miles  farther  from  Jupiter  than  our 
Moon  is  from  us ;  and  yet  this  second  moon  goes 
almost  eight  times  round  Jupiter  whilst  our  moon 
goes  only  once  round  the  Earth.  What  a  prodigious 
attractive  power  must  the  Sun  then  have,  to  draw  all 
the  planets  and  satellites  of  the  system  towards  him ! 
and  what  an  amazing  power  must  it  have  required  to 
put  all  these  planets  and  moons  into  such  rapid  mo- 
tions at  first !  Amazing  indeed  to  us,  because  impos- 
sible to  be  effected  by  the  strength  of  all  the  living 
creatures  in  an  unlimited  number  of  worlds ;  but  no 
ways  hard  for  the  ^taighty,  whose  planetarium  takes 
in  the  whole  universe. 

ARCH i-        159.  The  celebrated  ARCHIMEDES  affirmed  he 

MEbiem    COU^  move  tne  Earth,  if  he  had  a  place  at  a  dis- 

F™rlts?ng  tance  from  it  to  stand  upon  to  manage  his  machine- 

the  Earth.  ry,#.     This  assertion  is  true  h\  theory,  but,  upon 

examination,  will  be  found  absolutely  impossible  in 

fact,  even  though  a  proper  place,  and  materials  of 

sufficient  strength  could  be  had. 

The  simplest  and  easiest  method  of  moving  a 
heavy  body  a  little  way,  is  by  a  lever  or  crow ;  where 
a  small  weight  or  power  applied  to  the  long  arm 
will  raise  a  great  weight  on  the  short  one.  But 
then  the  small  weight  must  move  as  much  quicker 
than  the  great  weight,  as  the  latter  is  heavier  than 

*  AOJ  err*  JA),  x.a.i  rov  xo<r/xov  X^^TT,  z.  e.  Give  me  a  place  to  stand 
en,  and  I  shall  move  the  Earth. 


the  Planet?  Motions.  1 13 

the  former ;  and  the  length  of  the  long  arm  of  the 
lever  must  be  in  the  same  proportion  to  the  length 
of  the  short  one.  Now,  suppose  a  man  to  pull,  or 
press  the  end  of  the  long  arm  with  the  force  of 
200  pounds  weight,  and  that  the  Earth  contains  in 
round  numbers,  4,000, 000,000, 000,000,000,000, 
or  4000  trillions  of  cubit  feet,  each  at  a  mean  rate 
weighing  100  pound ;  and  that  the  prop  or  centre  of 
motion  of  the  lever  is  6000  miles  from  the  Earth's 
centre  :  in  this  case,  the  length  of  the  lever  from  the 
fulcrum  or  centre  of  motion  to  the  moving  power  or 
weight  ought  to  be  12,000,000,000,000,000,000,000, 
000,  or  12 quadrillions  of  miles;  and  so  many  miles  must 
the  power  move,  in  order  to  raise  the  Earth  but  one 
mile  ;  whence  it  is  easy  to  compute,  that  if  ARCHI- 
MEDES, or  the  power  applied,  could  move  as  swift  ' 
as  a  cannon  bullet,  it  would  take  27,000,000,000, 
000,  or  27  billions  of  years  to  raise  the  Earth  one 
inch. 

If  any  other  machine,  such  as  a  combination  of 
wheels  and  screws,  were  proposed  to  move  the  Earth, 
the  time  it  would  require,  and  the  space  gone  through 
by  the  hand  that  turned  the  machine,  would  be  the 
same  as  before.  Hence  we  may  learn,  that  however 
boundless  our  imagination  and  theory  may  be,  the 
actual  operations  of  man  are  confined  within  narrow 
bounds  ;  and  more  suited  to  our  real  wants  than  to 
our  desires. 

160.  The  Sun  and  planets  mutually  attract  each  Hard  to 
other :    the   power   by  which   they  do   so  we   call  determine 
gravity.  '  But  whether  this  power  be  mechanical  or^thya|9fr*' 
not,  is  very  much  disputed.  Observation  proves  that 
by  it  the  planets  disturb  one  another's  motions,  and 
that  it  decreases,  according  to  the  squares  of  the  dis- 
tances of  the  Sun  and  planets  inversely ;    as  light, 
which  is  known  to  be  material,  likewise  does.  Hence, 
gravity  should  seem  to  arise  from  the  agency  of  some 
subtle  matter  pressing  toward  the  Sun  and  planets, 
and  acting,  like  all  mechanical  causes,  by  contact. 


1 14  The  Physical  Causes  of 

But,  on  the  other  hand,  when  we  consider  that  the 
degree  or  force  of  gravity  is  exactly  in  proportion  to 
the  quantities  of  matter  in  those  bodies,  without  any 
regard  to  their  bulk  or  quantity  of  surface,  acting  as 
freely  on  their  internal  as  external  parts,  it  seems  to 
surpass  the  power  of  mechanism,  and  to  be  either  the 
immediate  agency  of  the  Deity,  or  effected  by  a  la\v 
originally  established  and  imprest  on  all  matter  by  him. 
But  some  affirm  that  matter,  being  altogether  inert, 
cannot  be  impressed  with  any  law,  even  by  Almighty 
power :  and  that  the  Deity,  or  some  subordinate  in- 
telligence, must  therefore  be  constantly  impelling  the 
planets  towards  the  Sun,  and  moving  them  with  the 
same  irregularities  and  disturbances  which  gravity 
would  cause,  if  it  could  be  supposed  to  exist.  >,  But, 
if  a  man  may  venture  to  publish  his  own  thoughts,  it 
seems  to  me  no  more  an  absurdity,  to  suppose  the 
Deity  capable  of  infusing  a  law,  or  what  law   he 
pleases,  into  matter,  than  to  suppose  him  capable  of 
giving  it  existence  at  first.     The  manner  of  both 
is  equally  inconceivable  to  us ;  but  neither  of  them, 
imply  a  contradiction  in  our  ideas :  and  what  implies 
no  contradiction  is  within  the  powder  of  Omnipotence. 

161.  That  the  projectile  force  was  at  first  given  by 
the  Deity  is  evident.     For  matter  can  never  put  it- 
self in  motion,  and  all  bodies  may  be  moved  in  any 
direction  whatever ;  and  yet  the  planets,  both  primary 
and  secondary,  move  from  west  to  east,  in  planes 
nearly  coincident ;  while  the  comets  move  in  all  di- 
rections, and  in  planes  very  different  from  one  an- 
other ;  these  motions  can  therefore  be  owing  to  no 
mechanical  cause  or  necessity,  but  to  the  free  will  and 
power  of  an  intelligent  Being. 

162.  Whatever  gravity  be,  it  is  plain  that  it  acts 
every  moment  of  time :  for  if  its  action  should  cease, 
the  projectile  force   w^ould  instantly  carry   off  the 


the  Planets'  Motions.  1 15 

planets  in  straight  lines  from  those  parts  of  their  or- 
bits where  gravity  left  them.  But,  the  planets  being 
once  put  into  motion,  there  is  no  occasion  for  any 
new  projectile  force,  unless  they  meet  with  some  re- 
sistance in  their  orbits ;  nor  for  any  mending  hand, 
unless  they  disturb  one  another  too  much  by  their 
mutual  attractions. 

163.  It  is  found  that  there  are  disturbances  among  The  pia- 
the  planets  in  their  motions,  arising  from  their  mutual  net*  &*- 

i  ,  .       ,  c  Ai      turb  one 

attractions,  when  they  are  in  the  same  quarter  or  the  another's 
heavens ;  and  the  best  modern  observers  find  that  our  motions, 
years  are  not  always  precisely  of  the  same  length*. 
Besides,  there  is  reason  to  believe  that  the  Moon  is 
somewhat    nearer    the   Earth  now  than     she   was 
formerly ;  her  periodical  month  being  shorter  than  it 
was  in  former  ages.     For  our  astronomical  tables,  Tjie  con. 
which  in  the  present  age  shew  the  times  of  solar  and  sequences 
lunar  eclipses  to  great  precision,  do  not  answer  so th 
well  for  very  ancient  eclipses.  Hence  it  appears,  that 
the  Moon  does  not  move  in  a  medium  void  of  all  re- 
sistance, ^  174  :  and  therefore  her  projectile  force  be- 
ing a  little  weakened,  while  there  is  nothing  to  dimi-  » 
nish  her  gravity,  she  must  be  gradually  approaching 
nearer  the  Earth,  describing   smaller  and   smaller 
circles  round  it  in  every  revolution,  and  finishing  her 
period  sooner,  although  her  absolute  motion  with  re- 
gard to  space  be  not  so  quick  now  as  it  was  formerly  : 
and,  therefore,  she  must  come  to  the  Earth  at  last ; 
unless  that  Being,  which  gave  her  a  sufficent  pro- 

*  If  the  planets  did  not  mutually  attract  one  another,  the  areas 
described  by  them  would  be  exactly  proportionate  to  the  times  of  de- 
scription, §  153.  But  observations  prove  that  these  areas  are  not  in 
such  exact  proportion,  and  are  most  varied  when  the  greatest  num- 
ber of  planets  are  in  any  particular  quarter  of  the  heavens.  When 
any  two  planets  are  in  conjunction,  their  mutual  attractions,  which 
tend  to  bring  them  nearer  to  one  another,  draw  the  inferior  one  a 
little  farther  from  the  Sun,  and  the  superior  one  a  little  nearer  t<. 
him ;  by  which  means,  the  figure  of  their  orbits  is  somewhat  altered; 
but  this  alteration  is  too  small  to  be  discovered  in  several  ages. 


116  Concerning  the  Nature  and 

jectile  force  at  the  beginning,  adds  a  little  more  to  it 
in  due  time.  And,  as  all  the  planets  move  in  spaces 
full  of  ether  and  light,  which  are  material  substances, 
they  too  must  meet  with  some  resistance.  And, 
therefore,  if  their  gravities  be  not  diminished,  nor 
their  projectile  forces  increased,  they  must  necessa- 
rily approach  nearer  and  nearer  the  Sun,  and  at  length 
fall  upon  and  unite  with  him. 

The  world  164.  Here  we  have  a  strong  philosophical  argu- 
not  eter-  ment  against  the  eternity  of  the'  YVorld.  For,  had  it 
existed  from  eternity,  and  been  left  by  the  Deity  to 
be  governed  by  the  combined  actions  of  the  above 
forces  or  powers,  generally  called  laws,  it  had  been 
at  an  end  long  ago.  And  if  it  be  left  to  them,  it  must 
come  to  an  end.  But  we  may  be  certain,  that  it  will 
last  as  long  as  was  intended  by  its  Author,  who 
ought  no  more  to  be  found  fault  with  for  framing  so 
perishable  a  work,  than  for  making  man  mortal*. 

CHAP.  VIII. 

Of  Light.  Its  proportional  Quantities  on  the  different 
Planets.  Its  Refractions  in  Water  and  Air.  The 
Atmosphere  ;  its  Weight  and  Properties.  The 
Horizontal  moon. 


I  A 


I  G  H  T  consists  of  exceeding  small  par- 
tides  of  matter  issuing  from  a  luminous 
body  ;    as,  from  a  lighted  candle  such  particles  of 
matter  constantly  flow  in  all  directions.    Dr.  NIEW- 
Theamaz-  ENTYxf  computes,  that  in  one  second  of  time  there 
ing  small-  flow   418,660,000,000,000,000,000,000,000,000, 
parUdes   000,000,000,000,000,   particles   of  light  out  of  a 
ofiight.    burning  candle;    which  number  contains   at   least 

*  M.  de  la  Grange  has  demonstrated,  on  the  soundest  principles  of 
philosophy*  that  the  solar  system  is  not  necessarily  perishable;  but 
that  the  seeming  irregularities  in  the  planetary  motions  oscillate,  as 
it  were,  within  narrow  lin.its  ;  and  that  the  world,  according  to  the 
present  constitution  of  nature,  may  be  permanent* 

t  Religious  Philosopher,  Vol.  HI.  p.  65. 


Properties  of  Light.  117 

6,337,242,000,000  times  the  number  of  grains  of 
sand  in  the  whole  Earth ;  supposing  100  grains  of 
sand  to  be  equal  in  length  to  an  inch,  and  consequent- 
ly, every  cubit  inch  of  the  Earth  to  contain  one  mil- 
lion of  such  grains. 

166.  These  amazingly  small  particles,  by  striking  The 
upon  our  eyes,  excite  in  our  minds  the  idea  of  light ;  ^ffccis"1 
and  if  they  were  as  large  as  the  smallest  particles  of  that  would 
matter  discernible  by  our  best  microscopes,  instead  * i?0sI^etheir 
of  being  serviceable  to  us,  they  would  soon  deprive  being 
us  of  sight,  by  the  force  arising  from  their  immenselarsel'- 
velocity ;  which  is  above  164  thousand  miles  every 
second*,  or  1,230,000  times  swifter  than  the  motion 
of  a  cannon  bullet.    And,  therefore,  if  the  particles  of 
light  were  so  large,  that  a  million  of  them  were  equal 
in  bulk  to  an  ordinary  grain  of  sand,  we  durst  no 
more  open  our  eyes  to  the  light,  than  suffer  sand  to 
be  shot  point  blank  against  them. 

167.  When  these  small  particles,  flowing  from  the  HOW  ob- 
Sun  or  from  a  candle,  fall  upon  bodies,  and  are  there-  jects  be- 
by  reflected  to  our  eyes,  they  excite  in  us  the  idea  of  S£to  us!" 
that  body,  by  forming  its  picture  on  the  retina  f.  And 

since  bodies  are  visible  on  all  sides,  light  must  be 
reflected  from  them  in  all  directions. 

168.  A  ray  of  light  is  a  continued  stream  of  these  The  rays 
particles,  flowing  from  any  visible  body  in  a  straight of h&ht 
line.     That  the  rays  move  in  straight,  and  not  in  movTi/ 
crooked  lines,  unless  they  be  refracted,  is  evident  s.trai^rM 
from  bodies  not  being  visible  if  we  endeavour  to  look lmes< 

at  them  through  the  bore  of  a  bended  pipe ;  and  from 
their  ceasing  to  be  seen  on  the  interposition  of  other 
bodies,  as  the  fixed  stars  by  the  interposition  of  the 
Moon  and  planets,  and  the  Sun  wholly  or  in  part  by 
the  interposition  of  the  Moon,  Mercury,  or  Venus.  A  proof 
And  that  these  rays  do  not  interfere,  or  jostle 


hinder  not 
one  ano- 


This  will  be  demonstrated  in  the  eleventh  chapter.  ther's 

t  A  fine  net-work  membrane  in  the  bottom  of  the  eye.  motions. 


118  Concerning  the  Nature  and 

Plate  IL  another  out  of  their  ways,  in  flowing  from  different 
bodies  all  around,  is  plain  from  the  following  experi- 
ment. Make  a  little  hole  in  a  thin  plate  of  metal,  and 
set  the  plate  upright  on  a  table,  facing  a  row  of  light- 
ed candles  standing  by  one  another;  then  place  a 
sheet  of  paper  or  pasteboard  at  a  little  dibtance  from 
the  other  side  of  the  plate,  and  the  rays  of  all  the 
candles,  flowing  through  the  hole,  will  lorm  as  many 
specks  of  light  on  the  paper  as  there  are  candles  be- 
fore the  plate ;  each  speck  as  distinct  and  large,  as  if 
there  were  only  one  candle  to  cast  one  speck  ;  which 
shews  that  the  rays  are  no  hindrance  to  each  other  in 
their  motions,  although  they  all  cross  in  the  hole. 

169.  Light,  and  therefore  heat,  so  far  as  it  depends 
on  the  Sun's  rays,  (§85,  toward  the  end,)  decreases 
in  the  inverse  proportion  of  the  squares  of  the  distances 
of  the  planets  from  the  Sun.     This  is  easily  demon- 
strated  by  a  figure;    which,  together  with  its  de- 
Fig.  XL    scription,  I  have  taken  from  Dr.  SMITH'S  Optics*. 
Let  the  light  which  flows  from  a  point  A,  and  passes 
through  a  square  hole  B,  be  received  upon  a  plane  C, 
in  what    parallel  to  the  plane  of  the  hole ;  or,  if  you  please,  let 
%hPtTndn  the  %ure  C  be  the  shadow  of  the  plane  B;  and  when 
Leat  de-    the  distance  C  is  double  of  B,  the  length  and  breadth 
crease  at  of  t^e  snaciow  C  will  be  each  double  of  the  length 
dwtan'ce"  and  breadth  of  the  plane  B ;  and  treble  when  AD  is 
from  the   treble  of  AB;   and  so  on  :    which  may  be   easily 
examined   by  the  light  of  a  candle  placed   at  A. 
Therefore  the   surface  of   the  shadow    C,    at   the 
distance  AC  double  of  AB,  is  divisible   into  four 
squares,  and  at  a  treble  distance,  into  nine  squares, 
severally  equal  to  the  square  B,  as  represented  in 
the  figure.     The  light,  then,  which  falls  upon  the 
plane   7?,   being   suffered  to   pass  to   double    that 
distance,  will  be  uniformly  spread  over  four  times 
the  space,    and   consequently   will    be  four  times 

*  Book  I.  Art.  57. 


Properties  of  Light.  119 

thinner  in  every  part  of  that  space  ;  at  a  treble  dis- Plate  n 
tance,  it  will  be  nine  times  thinner ;  and  at  a  quad- 
ruple distance,  sixteen  times  thinner,  than  it  was  at 
first ;  and  so  on,  according  to  the  increase  of  the 
square  surfaces  B,  C,  Z),  E,  described  upon  the 
distances  AB,  AC,  AD,  AE.  Consequently,  the 
quantities  of  this  rarefied  light  received  upon  a  sur- 
face of  any  given  size  and  shape  whatever,  removed 
successively  to  these  several  distances,  will  be  but 
one-fourth,  one-ninth)  one-sixteenth,  respectively,  of 
the  whole  quantity  received  by  it  at  the  first  distance 
AB.  Or,  in  general  words,  the  densities  and  quan- 
tities of  light,  received  upon  any  given  plane,  are 
diminished  in  the  same  proper  ion,  as  the  squares  of 
the  distances  of  that  plane,  from  the  luminous  body, 
are  increased  :  and  on  the  contrary,  are  increased  in 
the  same  proportion  as  these  squares  are  diminished. 

170.  The  more  a  telescope  magnifies  the  discs  of  why  the 

the  Moon  and  planets,   so  much  the  dimmer  they  Planets 

*  appeal- 
appear  than  to  the  bare  eye ;  because  the  telescope  dimmer 

cannot  magnify  the  quantity  of  light  as  it  does  the  ^hen 
surface ;  and,  by  spreading  the  same  quantity  of  light  through 
over  a  surface  so  much  larger  than  the  naked  eye  telescopes 
beheld,  just  so  much  dimmer  must  it  appear  when 
viewed  by  a  telescope,  than  by  the  bare  eye.  eye. 

171.  When  a  ray  of  light  passes  out  of  one  me- 
dium* into  another,  it  is  refracted,  or  turned  put  of 
its  first  course,  more  or  less,  as  it  falls  more  or  less 
obliquely  on  the  refracting  surface  which  divides  the 
two  mediums.     This  may  be  proved  by  several  ex- 
periments ;  of  which  we  shall  onlv  give  three  for  ex- 
ample's sake.     1.  In  a  bason,  FGH,  put  a  piece  of  Fig.  vm. 
money,  as  DB,  and  then  retire  from  it  to  A ;  that 

is,  till  the  edge  of  the  bason  at  E  just  hides  the 
money  from  your  sight ;   then  keeping  your  head 

*  A  medium,  in  this  sense,  is  any  transparent  body,  or  that  through 
which  the  rays  of  light  c;  n  '*ass;  as  water,  glass,  diamond,  air;  aiu' 
even  a  vacuum  is  sometimes  called  a  medium. 

Q 


120  Concerning  the  Atmosphere. 

steady,  let  another  person  fill  the  bason  gently  witk 

water.     As  he  fills  it,  you  will  see  more  and  more 

Refrao     of  the  piece  DB  ;  which  will  be  all  in  view  when  the 

i-l0's°offthe  bason  is  full>  and  aPPear  as  if  lifted  UP  to  C-     For 
light.0       the  ray  AEB,  which  was  straight  while  the  bason 

was  empty,  is  now  bent  at  the  surface  of  the  water 
in  J£,  and  turned  out  of  its  rectilineal  course  into 
the  direction  ED.  Or,  in  other  words,  the  ray 
DEK,  that  proceeded  in  a  straight  line  from  the 
edge  D  while  the  bason  was  empty,  and  wrent  above 
the  eye  at  A,  is  now  bent  at  E  ;  and  instead  of  going 
on  in  the  rectilineal  direction  DEK>  goes  in  the  an- 
gled direction  DEA,  and  by  entering  the  eye  at  A 
renders  the  object  DIJ  visible.  Or,  2dly,  Place  the 
bason  where  the  Sun  shines  obliquely,  and  observe 
where  the  shadow  of  the  rim  E  falls  on  the  bottom, 
as  at  B :  then  fill  it  with  water,  and  the  shadow  will 
fall  at  D  ;  which  proves  that  the  rays  of  light,  falling 
obliquely  on  the  surface  of  the  water,  are  refracted, 
or  bent  downward  into  it. 

172.  The  less  obliquely  the  rays  of  light  fall  upon 
the  surface  of  any  medium,  the  less  they  are  refract- 
ed ;  and  if  they  fall  perpendicularly  on  it,  they  are  not 
refracted  at  all.     For,  in  the  last  experiment,  the 
higher  the  Sun  rises,  the  less  will  be  the  difference 
between  the  places  where  the  edge  of  the  shadow 
falls  in  the  empty  and  in  the  full  bason.    And,  3dly, 
if  a  stick  be  laid  over  the  bason,  and  the  Sun's  rays 
be  reflected  perpendicularly  into  it  from  a  looking- 
glass,  the  shadow  of  the  stick  will  fall  upon  the  same 
place  of  the  bottom,  whether  the  bason  be  full  or 
empty. 

173.  The  denser  that  any  medium  is,  the  more  is 
light  refracted  in  passing  through  it. 

the  at-          174.  The  Earth  is  surrounded  by  a  thin  fluid 

rnosphere.  mass  of  matter,  called  the  air  or  atmosphere ',  which 

gravitates  to  the  Earth,  revolves  with  it  in  its  diurnal 

motion,  and  goes  round  the  Sun  with  it  every  year. 


Concerning  the  Atmosphere.  12i 

This  fluid  is  of  an  elastic  or  springy  nature,  and  its 
lowest  part,  being  pressed  by  the  weight  of  ajl  the 
air  above  it,  is  pressed  the  closest  together;  and 
therefore  the  atmosphere  is  densest  of  all  at  the 
Earth's  surface,  and  higher  up  becomes  gradually 
rarer.  "  It  is  well  known*  that  the  air  near  the  sur- 
face of  our  Earth  possesses  a  space  about  1200  times 
greater  than  water  of  the  same  weight.  And  there- 
fore, a  cylindric  column  of  air  1200  feet  high,  is  of 
equal  weight  with  a  cylinder  of  water  of  the  same 
breadth,  and  but  one  foot  high.  But  a  cylinder  of 
air  reaching  to  the  top  of  the  atmosphere  is  of  equal 
weight  with  a  cylinder  of  water  about  33  feet  highf  ; 
and  therefore,  if  from  the  whole  cylinder  of  air,  the 
lower  part  of  1200  feet  high  be  taken  away,  the  re- 
maining upper  part  will  be  of  equal  weight  with  a 
cylinder  of  water  32  feet,  high ;  wherefore,  at  the 
height  of  1200  feet  or  two  -furlongs,  the  weight  of 
the  incumbent  air  is  less,  and  consequently  the  rarity 
©f  the  compressed  air  is  greater,  than  near  the  Earth's 
surface,  in  the  ratio  of  33  to  32.  And  the  air,  at  all 
heights  whatever,  supposing  the  expansion  thereof 
to  be  reciprocally  proportional  to  its  compression 
(and  this  proportion  has  been  proved  by  the  experi- 
ments of  Dr.  Hooke  and  others)  will  be  set  down  in 
the  following  table  :  in  the  first  column  of  which 
you  have  the  height  of  the  air  in  miles,  whereof  4000 
make  a  semi-diameter  of  the  Earth ;  in  the  second 
the  compression  of  the  air,  or  the  incumbent  weight ; 
in  the  third  its  rarity  or  expansion,  supposing  gravity 
to  decrease  in  the  duplicate  ratio  of  the  distances 
from  the  Earth's  centre :  The  small  numeral  figures 
being  here  used  to  shew  what  number  of  ciphers 


*  NEWTON'S  system  of  the  World,  p.  120, 
t  This  is  evident  from  common  pumps. 


122 


Concerning  the  Atmosphere. 

must  be  joined  to  the  numbers  expressed  by  the 
larger  figures,  as  0.171224  for  0.000000000000000 
00*1224,  and  2695615  for  26956000000000000000. 


The  air's 
compres- 
sion and 
rarity  at 
different 
heights. 


AIR  '.i 

U  :j?ht. 

Comprc  ^sion. 

|      Expansion. 

(j    ' 

33  

.     .   1 

5 

10 
20 

17.8515  .  . 
9.6717  .  . 
2.852  .  .  . 

.    .  1.8486 
.    .  3.4151 
.11  571 

.40 
400 
4000 
40000 
400000 
4000000 
infinite. 

0.2525     . 
0.171224. 
0.10H4C5 
0.1921628 
0.2017895 
0.2129878 
0.212994l 

.  136.83 
2695615 
73907102 
26263189 
41798207 
33414209 
54622269 

From  the  above  table  it  appears  that  the  air  in 
proceeding  upward  is  ratified  in  such  manner,  that 
a  sphere  of  that  air  which  is  nearest  the  Earth  but 
of  one  inch  diameter,  if  dilated  to  an  equal  rarefac- 
tion with  that  of  the  air  at  the  height  of  ten  semi- dia- 
meters of  the  Earth,  would  fill  up  more  space  than 
is  contained  in  the  whole  heavens  on  this  side  the 
fixed  stars.  And  it  likewise  appears  that  the  Moon 
does  not  move  in  a  perfectly  free  and  unresisting 
medium;  although  the  air,  ;:t  a  height  equal  to  her 
distances,  is  at  least  340G19[)  times  thinner  than  at 
the  Earth's  surface ;  and  therefore  cannot  resist  her 
motion,  so  as  to  be  sensible,  in  many  ages, 
its  weight  175.  The  weight  of  the  air,  at  the  Earth's  sur- 
face,is  found  by  experiments  made  with  the  air-pump; 
and  also  by  the  quantity  of  mercury  that  the  atmos- 
phere balances  in  the  barometer  ;  in  which,  at  a  mean 
state,  the  mercury  stands  29-J  inches  high.  And  if 
the  tube  were  a  square  inch  wide,  it  would  at  that 
-height  contain  29£  cubic  inches  of  mercury,  which 


how 
found. 


Concerning  the  Atmosphere.  123 

is  just  15  pounds  weight;  and  so  much  weight  of 
air  every  square  inch  of  the  Earth's  surface  sustains ; 
and  consequently  every  square  foot  144  times  as 
much.  Now,  as  the  Earth's  surface  contains,  in 
round  numbers,  200,000,000  square  miles,  it  must 
contain  no  less  than  5,575,680,000,000,000  square 
feet;  which  being  multiplied  by  2160,  the  number 
of  pounds  on  each  square  foot,  amounts  to  12,043, 
468,800,000,000,000  pounds,  for  the  weight  of  the 
whole  atmosphere.  At  this  rate,  a  middle-sized  man, 
whose  surface  is  about  15  square  feet,  is  pressed  by 
32,400  pounds  weight  of  air  ail  around ;  for  fluids 
press  equally  up  and  down,  and  on  all  sides.  But, 
because  this  enormous  weight  is  equal  on  all  sides, 
and  counterbalanced  by  the  spring  of  the  air  diffused 
through  all  parts  of  our  bodies,  it  is  not  in  the  least 
degree  felt  by  us. 

176.  Oftentimes  the  state  of  the  air  is  such,  that  A  common 
we  feel  ourselves  languid  and  dull ;  which  is  com-  I^f^e 
monly  thought  to  be  occasioned  by  the  air's  being  weight  of 
foggy  and  heavy  about  us.     But  that  the  air  is  thenthe  air- 
too  light,  is  evident  from  the  mercury's  sinking  in 

the  barometer,  at  which  time  it  is  generally  found 
that  the  air  has  not  sufficient  strength  to  bear  up  the 
vapours  which  compose  the  clouds,  for  when  it  is 
otherwise,  the  clouds  mount  high,  and  the  air  is  more 
elastic  and  weighty  above  us,  by  which  means  it 
balances  the  internal  spring  of  the  air  within  us, 
braces  up  our  blotftl- vessels  and  nerves,  and  makes 
us  brisk  and  lively. 

177.  According  to  *  Dr.  KEILL,  and  other  astro-  without 
nomical  writers,  it  is  entirely  owing  to  the  atmos-  ^^^e 
phere  that  the  heavens  appear  bright  in  the   day-  heavens 
time.     For,  without  an  atmosphere,  only  that  part 

of  the  heavens  would  shine  in  which  the  Sun  was 
placed  :  and  if  we  could  live  without  air,  and  should  and 
turn  our  backs  toward  the  Sun,  the  whole  heavens 

twilight. 
*  See  his  Astronomy,  p.  232. 


124  Concerning  the  Atmosphere 

Plate  a.  would  appear  as  dark  as  in  the  night,  and  the  stars 
would  be  seen  as  clear  as  in  the  nocturnal  sky.  In 
this  case,  we  should  have  no  twilight ;  but  a  sudden 
transition  from  the  brightest  sun-shine  to  the  black- 
est darkness,  immediately  after  sun-set ;  and  from 
the  blackest  darkness  to  the  brightest  sun- shine,  at 
sun-rising ;  which  would  be  extremely  inconvenient, 
if  not  blinding,  to  all  mortals.  But,  by  means  of  the 
atmosphere,  we  enjoy  the  Sun's  light,  reflected  from 
the  aerial  particles,  for  some  time  before  he  rises, 
and  after  he  sets.  For,  when  the  Earth  by  its  rota- 
tion has  withdrawn  our  sight  from  the  Sun,  the  at- 
mosphere being  still  higher  than  we,  has  the  Sun's 
light  imparted  to  it ;  which  gradually  decreases  until 
he  has  got  18  .degrees  below  the  horizon ;  and  then, 
all  that  part  of  the  atmosphere  which  is  above  us  is 
dark.  From  the  length  of  twilight,  the  Doctor  has 
calculated  the  height  of  the  atmosphere  (so  far  as  it 
is  dense  enough  to  reflect  any  light)  to  be  about  44 
miles.  But  it  is  seldom  dense  enough  at  the  height 
of  two  miles  to  bear  up  the  clouds. 

5t  brings        178.  The  atmosphere  refracts  the  .Sun's  rays  so, 
the  Sun  in  as  f-o  bring  h'im  jn  sight  every  clear  day,  before  he 
fore  he      rises  in  the  horizon ;   and  to  keep  him  in  view  for 
and  some  minutes  after  he  is  really  set  below  it.  For,  at 
some  times  of  the  year,  we  see  the  Sun  ten  minutes 
after  he     longer  above  the  horizon  than  he  would  be  if  there 
were  no  refraction ;  and  above  six  minutes  every  day 
at  a  mean  rate. 

.«£.  ix.  179.  To  illustrate  this,  let  IEK  be  a  part  of 
the  Karth's  surface,  covered  with  the  atmosphere 
HGFC;  and  let  HEO  be  the  sensible  horizon* 
of  an  observer  at  E.  When  the  Sun  is  at  A,  really 
below  the  horizon,  a  ray  of  light,  AC,  proceeding 
from  him  comes  straight  to  C,  where  it  falls  on 
the  surface  of  the  atmosphere,  and  there  entering 
.a  denser  medium,  it  is  turned  out  of  its  rectilineal 

*  As  far  as  one  can  see  round  him  on  the  Earth, 


Concerning  the  Atmosphere*  125 

course  ACdG,  and  bent  down  to  the  observer's  eye 
at  E ;  who  then  sees  the  Sun  in  the  direction  of  the 
refracted  ray  Ede,  which  lies  above  the  horizon,  ai\d 
being  extended  out  to  the  heavens,  shtws  the  Sun 
at  B,  J  171. 

IbO.  The  higher  the  Sun  rises,  the  less  his  rays 
are  refracted,  because  they  fall  less  obliquely  on  the 
surface  of  the  atmosphere,  §  172..  Thus,  when  the 
Sun  is  in  the  direction  of  the  line  Ej'L  continued, 
he  is  so  nearly  perpendicular  to  the  surface  of  the 
Earth  at  E,  that  his  rays  are  but  very  little  bent 
from  a  rectilineal  course. 

181.  The  Sun  is  about  32|  min.  of  a  deg.  inThequa»- 
breadth,  when  at  his  mean  distance  from  the  Earth  ;  tity  of  re- 
and  the  horizontal  refraction  of  his  rays  is  33|  min.  fracUOIW 
which  being  more  than  his  whole  diameter,  brings 
all  his  disc  in  view,  when  his  uppermost  edge  rises 
in  the  horizon.     At  ten  deg.  height,  the  refraction 
is  not  quite  5  min. ;  at  20  deg.  only  2  min.  26  sec.; 
at  30  deg.  but  1  min.  32  sec. ;  and  at  the  zenith,  it 
is  nothing :  the  quantity  throughout,  is  shew  n  by  the 
following  table,  calculated  by  Sir  ISAAC  NEWTON, 


126 


Concerning  the  Atmosphere. 


182.  A  TABLE   shewing    the  Refractions  of  the 
Sun,  Moon,  and  Stars;   adapted  to  their 
aji/iarcnt  Altitudes. 

Appar. 

Retrac- 

A! 

i  \  e  frac- 

AP 

Refrac- 

Alt. 

tion. 

All 

tion. 

Alt. 

tion. 

0.    M. 

M.     S. 

D. 

vi.    s. 

D. 

M.     S. 

0        0 

33      45 

21 

2      18 

56 

0     3 

0      15 

30      24 

22 

2      11 

57 

0      35 

0      30 

27      35 

23 

2        5 

58 

0      34 

0      45 

25      11 

24 

1      59 

59 

0      32 

1        0 

23        7 

25 

1      54 

60 

0      31 

1       15 

21      20 

26 

1      49 

61 

0      30 

1      30 

19      46 

27 

1      44 

62 

0     28 

1      45 

18      22 

28 

1      40 

63 

0     27 

2        0 

17        8 

29 

1      36 

64 

0      26 

2      30 

15        2 

30 

1      32 

65 

0      25 

3        0 

13      20 

3  1 

i      28 

66 

0     24 

3      30 

11      57 

32 

1      25 

67 

0      23 

4        0 

10     48 

3 

1      22 

68 

0     22 

4     30 

9      50 

34 

1      19 

69 

0      21 

5        0 

9        2 

35 

1      16 

70 

0      20 

5      30 

8      21 

36 

1       13 

71 

0      19 

6        0 

7      45 

37 

1      11 

72 

0      18 

6      30 

7      14 

38 

1        8 

73 

0      17 

7        0 

6      47 

39 

1         6 

74 

0      16 

7     30 

6      22 

40 

1        4 

75 

0      15 

8        0 

6        0 

4! 

1        2 

76 

0      14 

8      30 

5      40 

42 

1        0 

77 

0      13 

9        0 

5      22 

43 

0      58 

78 

0      12 

9      30 

5        6 

44 

0      56 

79 

0      11 

10       0 

4      52 

45 

0      54 

80 

0      10 

11        0 

4      27 

46 

0      52 

81 

0        9 

12        0 

4        5 

47 

0      50 

82 

0        8 

13        0 

3      47 

48 

0      48 

83 

0        7 

14        0 

3     31 

49 

0      47 

84 

0        6 

15        0 

3      17 

50 

0      45 

85 

0        5 

16        0 

3       4 

51 

0      44 

8n 

0        4 

17        0 

2     53 

52 

0      42 

87 

0        3 

18        0 

2      43 

53 

0      40 

88 

0        2 

19        0 

2      34 

54 

0      39 

89 

0         1 

20        0 

2      26 

55 

o    r^\    ;•;. 

0        0  , 

Concerning  the  Atmosphere.  127 

183.  In  all  observations,  to  obtain  the  true  alti- Plate  n* 
tude  of  the  Sun,    Moon,    or  stars,  the  refraction 
must  be  subtracted  from  the  observed  altitude.  But 
the  quantity  of  refraction  is  not  always  the  same  of  refrac- 
at  the  same  altitude;  because  heat  diminishes  thetu 
air's  refractive  power  and  density,  and  cold  increases 
both ;  and  therefore  no  one  table  can  serve  precisely 
for  the  same  place  at  all  seasons,  nor  even  at  all 
times  of  the  same  day,  much  less  for  different  cli- 
mates ;  it  having  been  observed  that  the  horizontal 
refractions  are  near  a  third  part  less  at  the  equator 
than  at  Paris.     This  is  mentioned  by  Dr.  SMITH 
in  the  37()th  remark  on  his  Optics,  where  the  follow- 
ing account  is  given  of  an  extraordinary  refraction 
of  the  Sun-beams  by  cold.     u  There  is  a  famous  A  very  re- 
observation  of  this  kind  made  by  some  Hollanders  markabie 
that  wintered  mNova-Zembia  in  the  year  1596,  who^^J^f" 
were  surprised  to  find,  that  after  a  continual  night  rcfrac- 
of  three  months,  the  Sun  began  to  rise   seventeen tl( 
days  sooner  than  according  to  computation,  dedu- 
ced from  the  altitude  of  the  pole,  observed  to  be  76° ; 
which  cannot  otherwise  be  accounted  for,  than  by 
an  extraordinary  refraction  of  the  Sun's  rays  passing 
through  the  cold  dense  air  in  that  climate.     Kepler* 
computes  that  the  Sun  was  almost  five  degrees  be- 
low  the  horizon  when  he  first  appeared ;  and  conse- 
quently the  refraction  of  his  rays  was  about  nine 
times  greater  than  it  is  with  us." 

184.  The  Sun  and  Moon  appear  of  an  oval  figure, 
as  FCGD,  just  after  their  rising,  and  before  their  Fig.  x. 
setting :  the  reason  of  which  is,— the  refraction  be- 
ing greater  in  the  horizon  than  at  any  distance  above 
it,  the  lower  limb  G  is  more  elevated  by  it  than  the 
upper.  But  although  the  refraction  shortens  the 
vertical  diameter  FG,  it  has,  no  sensible  effect  on  the 
horizontal  diameter  CZ),.  which  is  all  equally  elevat- 
ed. When  the  refraction  is  so  small  as  to  be  im- 


128  Concerning  the  Atmosphere. 

perceptible,   the  Sun  and  Moon    appear  perfectly- 
round,  as  A  E  B  F. 

°ination "      *^5'  When  we  have  nothing  but  our  imagination  to 
fannotn    assist  us  in  estimating  distances,  we  are  liable  to  be 
judge       deceived ;   for  bright  objects  seem  nearer  to  us  than 
-  ^lose  which  are  less  bright,  or  than  the  same  objects 
do  when  they  appear  less  bright  and  worse  denned, 
even  though  their  distance  be  the  same.    And  if  in 
jects ;       both  cases  they  are  seen  under  the  same  angle*,  our 
imagination  naturally  suggests  an  idea  of  a  greater 
distance  between  us  and  those  objects  which  appear 
fainter  and  worse  defined  than  those  which  appear 
brighter  under  the  same  angles;  especially  if  they 
be  such  objects  as  we  were  never  near  to,  and  of 
whose  real  magnitudes   we  can  be  no  judges  by 
sight. 

186.  But  it  is  not  only  in  judging  of  the  different 
apparent  magnitudes  of  the  same  objects,  which 
are  better  or  worse  defined  by  their  being  more  or 
less  bright,  that  wre  may  be  deceived :  for  we  may 
make  a  wrong  conclusion  even  when  we  view  them 


nor  at-  *  ^ne  nearer  an  object  is  to  the  eye?  the  bigger  it  appears,  and 

•ways  of  **  is  seen  Hnder  the  greater  angle.  To  illustrate  this  a  little,  suppose 
those  an  arrow  in  thc  position  IK,  perpendicular  to  the  right  line  HA, 
•which  are  drawn  n'om  tne  eve  at  H  through  the  middle  of  the  arrow  at  O.  It 
accessi-  ls  V}am  tVat  tne  arrow  is  seen  under  the  angle  IHK,  and  that  HO, 
kk  -which  is  its  distance  from  the  eye,  divides  mto  halves  both  the  ar- 

row and  the  angle  under  which  it  is  seen,  v/z.  the  arrow  into  1O, 
OK;  and  the  angle  into  I  HO  and  KHO:  and  this  will  be  the 
case  at  whatever  distance  the  arrow  is  placed;  Let  now  three  ar- 
rows, all  of  the  same  length  with  IK,  be  placed  at  the  distances 
HA,  HCK,  H,  still  perpendicular  to,  and  bisected  by  the  right 
line  HA;  then  will  AB,  CD,  EF,  be  each  equal  to,  and  represent 
O  I;  and  A  B  (the  same  as  OI)  will  be  seen  Irom  H  under  the  angle 
AHB  ;  but  CD  (the  same  as  OI)  will  be  seen  under  the  angle  CHD, 
or  A.HL;  and  RF(\\\z  same  as  OI)  will  be  seen  under  the  angle 
•jL'l-1^  or  C7/A,  or  AHM.  Also  EF.  or  OI,  at  the  distance  HE, 
will  appear  as  long  as  ON  wruld  at  the  distance  HC,  or  as  AM 
would  at  the  distance  HA;  and  CD,  or  7O,at  the  distance  HC,  will 
appear  as  long  as  AL  would  at  the  distance  HA.  So  that  as  an  ob- 
ject approaches  the  eye,  both  its  nsagnitude  and  the  angle  under 
which  it  is  seen  increase ;  and  the  contrary  as  the  object  recedes. 


The  Phenomena  of  the  Horizontal  Mow,  £cc. 

under  equal  degrees  of  brightness,  and  under  equal 
angles;  although  they  be  objects  whose  bulks  we  are 
generally  acquainted  with,  such  as  houses  or  trees ; 
for  proof  of  which,  the  two  following  instances  may 
suffice : 

First,  When  a  house  is  seen  over  a  very  broad  The 
river  by  a  person  standing  on  a  low  ground,  who 
sees  nothing  of  the  river,  nor  knows  of  it  before- 
hand ;  the  breadth  of  the  river  being  hid  from  him, 
because  the  banks  seem  contiguous,  he  loses  the 
idea  of  a  distance  equal  to  that  breadth ;  and  the 
house  seems  small  because  he  refers  it  to  a  less  dis- 
tance than  it  really  is  at.  But  if  he  goes  to  a  place 
from  which  the  river  and  interjacent  ground  can  be 
seen,  though  no  farther  from  the  house,  he  then  per- 
ceives  the  house  to  be  at  a  greater  distance  than  he 
bad  imagined ;  and  therefore  fancies  it  to  be  bigger 
than  he  did  at  first ;  although  in  both  cases  it  ap- 
pears under  the  same  angle,  and  consequently  makes 
no  bigger  picture  on  the  retina  of  his  eye  in  the  lat- 
ter case  than  it  did  in  the  former.  Many  have  been 
deceived  by  taking  a  red  coat-of-arms,  fixed  upon 
the  iron  gate  in  Clare -Hall  walks  at  Cambridge ,  for 
a  brick  house  at  a  much  greater  distance.*  Pia# 

Secondly,  In  foggy  weather,  at  first  sight,  we 
generally  imagine  a  small  house  which  is  just  at 


*  The  fields  which  are  beyond  the  gate  rise  gradually  till  they  are 
just  seen  over  it ;  and  the  arms  being  red,  are  often  mistaken  for  a 
house  at  a  considerable  distance  in  those  fields. 

I  once  met  with  a  curious  deception  in  a  gentleman's  garden  at 
Hackney^  occasioned  by  a  large  pane  of  glass  in  the  garden  wall  at 
some  distance  from  his  house.  The  glass  (through  which  the  sky 
was  seen  from  low  ground)  reflected  a  very  faint  image  of  the  house ; 
but  the  image  seemed  to  be  in  the  clouds  near  the  horizon,  and  at 
that  distance  looked  as  if  k  were  a  huge  castle  in  the  air.-^Yet  the 
angle,  under  which  the  image  appeared,  was  equal  to  that  under 
which  the  house  was  seen :  but  the  image  being  mentally  referred 
to  a  much  greater  distance  than  the  house,  appeared  much  bigger 
to  the  imagination. 


130  The  Phenomena  of  the 

Plate  1L  hand,  to  be  a  great  castle  at  a  distance ;  because  ft 
appears  so  dull  and  ill-defined  when  seen  through 
the  mist,  that  we  refer  it  to  a  much  greater  distance 
than  it  really  is  at ;  and  therefore,  under  the  same 
Fig-  xu  an&k'>  we  judge  it  to  be  much  bigger.  For,  the 
near  object  FE,  seen  by  the  eye  A  B  D,  appears 
under  the  same  angie  GC77that  the  remote  obiect 
G///does;  and  the  rays  GFCN  and  HECM, 
crossing  one  another  at  C  in  the  pupil  oi  the  eye, 
limit  the  size  of  the  picture  MN  on  the  retina, 
which  is  the  picture  of  the  object  FE;  and  if  FE 
were  taken  away,  would  be  the  picture  of  the  ob- 
ject £///,  only  worse  defined ;  because  GHI  being 
farther  off,  appears  duller  and  fainter  than  FE  did. 
But  when  a  fog,  as  KL^  comes  between  the  eye 
and  the  object  FE,  the  object  appears  dull  and  ill- 
defined  like  GHI;  which  causes  otir  imagination  to 
refer  FE  to  the  greater  distance  C//,  instead  of  the 
small  distance  CJ5,  which  it  really  is  at.  And  con* 
sequently,  as  misjudging  the  distance  does  not  in 
the  least  diminish  the  angle  under  which  the  object 
appears,  the  small  hay-rick  FE  seems  to  be  as  big 
as  GHL 

Fig.  ix.         187.  The  Sun  and  Moon  appear  bigger  in  the 

horizon  than  at  any  considerable   height  above  it. 

These  luminaries,  although  at  great  distances  from 

the  Earth,  appear  floating,  as  it  were,  on  the  surface 

of  our  atmosphere  HG  Ffe  C,  a  little  way  beyond 

Whyfhe  tne  clouds;  of  which  those  about  Fy  directly  over 

Sun  and    our  heads  at  £,  are  nearer  us  than  those  about  77  or 

™arnbiag."  e  in  the  horizon  HEe.     Therefore,  when  the  Sun 

g-est  in  the  or  Mopn  appears  in  the  horizon  at  e,  they  are  not 

honzon,    onjy  seen  ^n  a  part  of  tke  skV)  which  is  really  farther 

from  us  than  if  they  were  at  any  considerable  alti- 
tude, as  about/;  but  they  are  also  seen  through  a 
greater  quantity  of  air  and  vapours  at  e  than  at  f. 
Here  we  have  two  concurring  appearances  which  de- 
ceive our  imagination,  and  cause  us  to  refer  the  Sun 


Horizontal  Moon  explained.  131 

and  Moon  to  a  greater  distance  at  their  rising  or  setting 
about  e ,  than  when  they  are  considerably  high  as  atyV 
first,  their  seeming  to  be  on  a  part  of  the  atmosphere 
at  (?,  which  is  really  farther  than^'from  a  spectator  at 
Ef  and  secondly,  their  being  seen  through  a  grosser 
medium,  when  at  ey  than  when  aty/  which,  by  ren- 
dering them  dimmer,  causes  us  to  imagine  them  to 
be  at  a  yet  greater  distance.  And  as,  in  both  cases, 
they  are  seen*  much  under  the  same  angle,  we  na- 
turally judge  them  to  be  biggest  when  they  seem 
farthest  from  us ;  like  the  abovementioned  house, 
§  186,  seen  from  a  higher  ground,  which  shewed  it 
to  be  farther  off  than  it  appeared  from  low  ground; 
or  the  hay -rick,  which  appeared  at  a  greater  distance 
by  means  of  an  interposing  fog. 

188.  Any  one  may  satisfy  himself  that  the  Moon  Their  ap- 
appears  under  no  greater  angle  in  the  horizon  than  parent  di- 
on  the  meridian,  by  taking  a  large  sheet  of  paper,  are^ot* 
and  rolling  it  up  in  the  form  of  a  tube,  of  such  a  less  on  the 
width,  that  observing  the  Moon  through  it  when  she 

rises,  she  may,  as  it  were,  just  fill  the  tube ;  then  tie  horizon, 
a  thread  round  it  to  keep  it  of  that  size ;  and  when 
the  Moon  comes  to  the  meridian,  and  appears  much 
less  to  the  eye,  look  at  her  again  through  the  same 
tube,  and  she  will  fill  it  just  as  much,  if  not  more, 
than  she  did  at  her  rising. 

189.  When  the  full  Moon  is  in  perigee,  or  at  her 
least  distance  from  the  Earth,  she  is  seen  under  a 
larger  angle,  and  must  therefore  appear  bigger  than 
when  she  is  full  at  other  times ;  and  if  that  part  of  the 
atmosphere   where  she  rises  be  more  replete  with 

*  The  Sun  and  Moon  subtend  a  greater  angle  on  the  meridian 
than  in  the  horizon,  being  nearer  the  observer's  place  in  the  forme*- 
case  than  in  the  latter, 


The  Method  of  finding  the  Distances 

vapours  than  usual,  she  appears  so  much  the  dim- 
mer ;  and  therefore  we  fancy  her  to  be  still  the  big- 
ger,  by  referring  her  to  an  unusually  great  distance, 
knowing  that  no  objects  which  are  very  far  distant 
can  appear  big  unless  they  be  really  so. 


CHAP.  IX. 


Hie  Method  of  finding  the  Distances  of  the  Sun, 
Moon,  and  Planets, 

,QQ  Y  |  ^HOSE  who  have  not  learnt  how  to  take 
J[_     the  #  altitude  of  any  celestial  phenome- 
non by  a  common  quadrant,  nor  know  any  thing  of 
plane  trigonometry,  may  pass  over  the  first  article  of 
this  short  chapter,  and  take  the  astronomer's  word 
for  it,  that  the  distances  of  the  Sun  and  planets  are 
as  stated  in  the  first  chapter  of  this  book.     But,  to 
every  one  who  knows  how  to  take  the  altitude  of  the 
Sun,  the  Moon,  or  a  star,  and  can  solve  a  plane  right 


*  The  altitude  of  any  celestial  object,  is  an  arc  of  the  sky  intercep- 
ted between  the  horizon  and  the  object.  In  Fig.  VI.  of  Plate  //.  let 
HOX  be  a  horizontal  line,  supposed  to  be  extended  from  the  eye  at 
A  to  X)  where  the  sky  and  Earth  seem  to  meet  at  the  end  of  a  long 
and  level  plane;  and  let  5  be  the  Sun.  The  arc  AY  will  be  the 
Sun's  height  above  the  horizon  at  Xy  and  is  found  by  the  instrument 
JSCD,  which  is  a  quadrantal  board,  or  plate  of  metal,  divided  into 
90  equal  parts  or  dcgives  on  its  limb  DPC,  and  has  a  couple  of  lit- 
tle brass  plates,  as  a  and  £,  with  a  small  hole  in  each  of  them,  call- 
ed sight-holes,  tor  looking  through,  parallel  to  the  edge  of  the  quad- 
rant which  they  stand  on.  To  the  centre  JS,  is  fixed  one  end  of  a 
thread  1>\  called  the  plumb-line,  which  has  a  small  weight  or  plum- 
met P  fixed  to  its  other  end.  Now,  if  an  observer  hold  the  quad- 
rant upright,  without  inclining  it  to  either  side,  and  so  that  the  hori- 
zon at  X  is  seen  through  the  sight-holes  a  and  6,  the  plumb-iine  will 
cut  or  hang  over  the  beginning  of  the  degrees  at  0,  in  the  edge  JiC ; 
but  if  he  elevate  the  quadrant  so  as  to  look  through  the  sight-holes 
at  any  part  of  the  heavens,  suppose  the  Sun  at  S^just  so  many  de- 
grees as  he  elevates  the  sight-hole  b  above  the  horizontal  line  HOX, 


vf  the  Sun,  Moon,  and  Planets.  13o 

ingled  triangle,  the  following  method  of  finding  the  Plate  tv. 
distances  of  the  Sun  and  Moon  will  be  easily  under- 
stood. 

Let  BAG  be  one  half  of  the  Earth,  AC  its  semi-  Fr  L 
diameter,  «$'  the  Sun,  m  the  Moon,  and  EKOL  a 
quarter  of  the  circle  described  by  tlie  Moon  in  re- 
volving from  the  meridian  to  the  meridian  again. — 
Let  CjRiS  be  the  rational  horizon  of  an  observer  at 
A,  extended  to  the  Sun  in  the  heavens ;  and  HAG 
his  sensible  horizon,  extended  to  die  Moon's  orbit. 
ALC  is  the  angle  under  which  the  Earth's  semidi- 
ameter^C*  is  seen  from  the  Moon  at  Ly  which  is  equal 
to  the  angle  OAL,  because  the  right  lines  AO  and 
CLj  which  include  both  these  angles,  are  parallel. 
ASCis  the  angle  under  which  the  Earth's  semidiame- 
ter  AC  is  seen  from  the  Sun  at  -S9  and  is  equal  to 
the  angle  OAf;  because  the  lines  AO  and  CRS  are 
parallel.  Now,  it  is  found  by  observation,  that  the 
angle  OAL  is  much  greater  than  the  angle  OAf; 
but  OAL  is  equal  to  ALC\  and  OAf  is  equal  to 
ASC.  Now,  asASC  is  much  less  than  ALC,  it 
proves  that  the  Earth's  semidiameter  AC  appears 
much  greater  as  seen  from  the  Moon  at  Z/,  than 
from  the  Sun  at  S ;  and  therefore  the  Earth  is  much 
farther  from  the  Sun  than  from  the  Moon.*  The 


•so  many  degrees  -will  the  plumb-line  cut  in  the  limb  CP  ot  the  quad- 
rant. For,  let  the  observer's  eye  at  A  be  in  the  centre  of  the  celes- 
tial arc  XY7,  (and  he  may  be  said  to  be  in  the  centre  of  the  Sun's 
apparent  diurnal  orbit,  tet  him  be  on  what  part  of  the  Earth  he  will) 
in  which  arc  the  Sun  is  at  that  time,  suppose  25  degrees  high,  and  let 
the  observer  hold  the  quadrant  so  that  he  may  see  the  Sun  through 
the  sight-holes;  the  plumb-line  freely  playing  on  the  quadrant  will 
cut  the  25th  degree  in  the  limb  C1/*,  equal  to  the  number  of  degrees 
of  the  Sun's  altitude  at  the  time  of  observation* 

.'V*.  /?.  Whoever  looks  at  the  Sun  must  have  a  smoked  glass  be- 
fore his  eyes  to  save  them  from  hurt.  The  better  way  is  not  to  look 
at  the  Sun  through  the  sight-holes,  but  to  hold  the  quadrant  facing 
the  eye  at  a  little  di&tance,  and  so  that  the  Sun  shining  through  one 
hole,  the  ray  may  be  seen  to  fall  on  the  other. 

*  See  the  Note  on  $  185-. 


134  The  Method  of  finding  the  Distances 

quantities  of  these  angles  may  be  determined  by  ob- 
servation in  the  following  manner ; 

Let  a  graduated  instrument,  as  DAE,  (the  larg- 
er the  better^)  having  a  moveable  Index  with  sight- 
holes,  be  fixed  in  such  a  manner,  that  its  plane  sur- 
face may  be  parallel  to  the  plane  of  the  equator,  and  its 
edge  AD  in  the  plane  of  the  meridian :  so  that  when  the 
Moon  is  in  the  equinoctial,  and  on  the  meridian 
ADE,  she  may  be  seen  through  the  sight-holes 
when  the  edge  of  the  moveable  index  cuts  the  be- 
ginning of  the  divisions  at  0,  on  the  graduated  limb 
DE;  and  when  she  is  so  seen,  let  the  precise  time 
be  noted.  Now,  as  the  Moon  revolves  about  the 
Earth  from  the  meridian  to  the  meridian  again  in 
about  24  hours  48  minutes,  she  will  go  a  fourth 
part  round  it  in'  a  fourth  part  of  that  time,  viz.  in 
six  hours  twelve  minutes,  as  seen  from  C,  that  is, 
from  the  Earth's  centre  or  pole.  But  as  seen  from 
A,  the  observer's  place  on  the  Earth's  surface,  the 
Moon  will  seem  to  have  gone  a  quarter  round  the 
Earth  when  she  comes  to  the  sensible  horizon  at  0; 
for  the  index  through  the  sights  of  which  she  is  then 
viewed,  will  be  at  </,  90  degrees  from  D,  where  it 
was  when  she  was  seen  at  E*  Now  let  the  exact 
moment  when  the  Moon  is  seen  at  O  (which  will  be 
when  she  is  in  or  near  the  sensible  horizon)  be  care- 
fully noted*,  that  it  may  be  known  in  what  time  she 
has  gone  from  E  to  O  ;  which  time  subtracted  from 
6  hours  12  minutes  (the  times  of  her  going  from  E 
The  to  L)  leaves  the  time  of  her  going  from  0  to  _£, 
Moon's  ancj  affords  an  easy  method  for  finding  the  angle 
parHiiu  OAL,  (called  the  Moon's  horizontal  parallax,  which 
what.  is  equal  to  the  angle  ALCJ  by  the  following  analo- 


*  Here  proper  allowance  must  be  made  for  the  refraction,  which 
being  about  34  minutes  of  a  degree  in  the  horizon,  will  cause  the 
moon's  centre  to  appear  34  minutes  above  the  horizon  when  her  cen- 
tre is  really  in  iU 


of  the  Sun,  Moon,  and  Planets.  135 

gy  :  As  the  time  of  the  Moon's  describing  the  arc 
EO  is  to  90  degrees,  so  is  6  hours  12  minutes  to 
the  degrees  of  the  arc  Dele,  which  measures  the  an- 
gle EAL ;  from  which  subtract  90  degrees,  and 
there  remains  the  angle  OAL,  equal  to  the  angle 
ALC,  under  which  the  Earth's  semi- diameter  AC  is 
seen  from  the  Moon.  Now,  since  all  the  angles  of  a 
right-lined  triangle  are  together  equal  to  180  degrees, 
or  to  two  right  angles,  and  the  sides  of  a  triangle  are  al- 
ways proportional  to  the  sines  of  the  opposite  an-  The 
gles,  say  by  the  Rule  of  Three,  as  the  sine  of  the  Moon's 
ande  ALC,  at  the  Moon  L,  is  to  its  opposite  side  distance 

^Pt     i       -r«       i  ,  •    T  i  •   i     •     i  determm* 

AL,  the  Earth's  semi-diameter,  which  is  known  toe(j. 
be  3985  miles,  so  is  radius,  viz.  the  sine  of  90  de- 
grees, or  of  the  right  angkylLC,  to  its  opposite  side 
AD,  which  is  the  Moon's  distance  at  L  from  the 
observer's  place  at  A,  on  the  Earth's  surface ;  or,  so 
is  the  sine  of  the  angle  CAL  to  its  opposite  side  CL, 
which  is  the  Moon's  distance  from  the  Earth's  cen- 
tre, and  comes  out  at  a  mean  rate  to  be  240,000 
miles.  The  angle  CAL  is  equal  to  what  OAL  wants 
of  90  degrees. 

191.  The  Sun's  distance  from  the  Earth  ^ghtj^ance'* 
be  found  in  the  same  way,  though  with  more  diffi-  cannotCbe 
culty,  if  his  horizontal  parallax,  or  the  angle  OAS,  yet  so  ex- 
equal  to  the  angle  ASC,  were  not  so  small,  as  tobe^ermined 
hardly  perceptible;  being  scarce  10  seconds  of  a  as  the 
minute,    or   the   360th   part  of   a  degree.      ButMoon'*4 
the   Moon's  horizontal  parallax,   or  angle  OAL, 
equal    to  the   angle    ALC,    is    very   discernible, 
being  57'  18",  or  3438"  at  its  mean  state;  which 
is  more  than  340  times  as  great  as  the  Sun's  :  and, 
therefore,  the  distances  of  the  heavenly  bodies  being 
inversely  as  the  tangents  of  their  horizontal  parallax- 
es, the  Sun's  distance  from  the  Earth  is  at  least  340 
times  as  great  as  the  Moon's :   and  is  rather  under- 
rated at  81  millions  of  miles,  when  the  Moon's  dis- 
tance is  certainly  known  to  be  240  thousand.    But 

S 


136  The  Method  of  finding  the  Distances 

because,  according  to  some  astronomers,  the  Sun's 
horizontal  parallax,  is  11  seconds,  and  according  to 
others  only  10,  the  former  parallax  making  the  Sun's 
distance  to  be  about  75,000,000  of  miles,  and  the 
latter  82,000,000 ;  we  may  take  it  for  granted  that 
the  Sun's  distance  is  not  less  than  as  deduced  from 
the  former,  nor  more  than  as  shewn  by  the  latter : 
and  every  one,  who  is  accustomed  to  make  such  ob- 
servations, knows  how  hard-  it  is,  if  not  impossible, 
to  avoid  an  error  of  a  second,  especially  on  account 
of  the  inconstancy  of  horizontal  refractions.  And 
here  the  error  of  one  second,  in  so  small  an  angle, 
will  make  an  error  of  7  millions  of  miles  in  so  great 
a  distance  as  that  of  the  Sun's.  But  Dr.  HAL  LEY 
has  shewn  us  how  the  Sun's  distance  from  the  Earth, 
and  consequently  the  distances  of  all  the  planets 
How  near  from  the  Sun,  may  be  known  to  within  a  500th 
the  truth  part  of  the  whole,  by  a  transit  of  Venus  over  the 
soorTbe  S«n's  disc,  which  will  happen  on  the  6th  of  June, 
determine  in  the  year  1761 ;  till  which  time  we  must  content 
ourselves  with  allowing  the  Sun's  distance  to  be  a- 
bout  81  millions  of  miles,  as  commonly  stated  by 
astronomers. 

Sun        "^'  ^ke  ^un  anc*Moon  appear  much  about  the 
provetUo  same  bulk ;  and  every  one  who  understands  geom- 
b^  much   etry,  knows  how  their  true  bulks  may  be  deduced 
thaifthe    fr°m  ^ie  apparent,  when  their  real   distances  are 
Moon.      known.     Spheres  are  to  one  another  as  the  cubes  of 
their  diameters;  whence,  if  the  Sun  be  81  millions 
of  miles  from  the  Earth,  to  appear  as  big  as  the 
Moon,  whose  distance  does  not  exceed  240  thou- 
sand miles,  he  must  in  solid  bulk  be  42  millions 
875  thousand  times  as  big  as  the  Moon. 

193.  The  horizontal  parallaxes  are  best  observed 
at  the  equator;  1.  Because  the  heat  is  so  nearly 


of  the  Sun,  Moon,  and  Planets.  13~ 

equal  every  dayv  that  the  refractions  are  almost  con- 
stantly the  same.  2.  Because  the  parallactic  angle 
is  greater  there,  as  at  A,  (the  distance  from  thence  to 
the  Earth's  axis  being  greater,)  than  upon  any  par- 
allel of  latitude,  as  a  or  b. 

194.  The  Earth's  distance  from  the  Sun  being  The  rek- 
determined,  the  distances  of  all  the  other  planets  JancesSof 
from  him  are  easily  found  by  the  following  analogy,  the  pian- 
their  periods  round  him  beiner  ascertained  by  obser-  e,ts  *5om 

•  A          i  p      i          r»         i  •       1  i  **le  -5U11 

vation.     As  the  square  ot  the  karth 's  period  round  are  known 
the  Sun,  is  to  the  cube  of  its  distance  from  the  Sun ; to  S1'6^ 
so  is  the  square  of  the  period  of  any  other  planet,  to  though.0"' 
the  cube  of  its  distance  in  such  parts  or  measurestheirreal 
as  the  Earth's  distance  was  taken;  see  §111.  This  *f  *n0ctes 
proportion  gives  the  relative  mean  distances  of  the  well 
planets  from  the  Sun  to  the  greatest  degree  of  ex-knowa 
actness.     They  are  as  follows,  having  been  dedu- 
ced from  their  periodical  times ;  according  to  the  law 
just  mentioned,  which  was  discovered  by  KEPLER, 
and  demonstrated  by  Sir  ISAAC  NEWTON,* 


*  All  the  following  calculations  except  those  in  the  two  last  lines 
before  §  195,  were  printed  informer  editions  of  this  work,  before  the 
year  1761.  Since  that  time  the  said  two  lines  (as  found  by  the  tran- 
sit A.  D.  17611  were  added ;  and  also  §  195. 


138  The  Periods  and  Distances  of  the  Planets. 

Periodical  Revolutions  to  the  same  fixed  Star,  in 
Days  and  Decimal  Parts  of  a  day. 

Mercury    I      Venus      I  The  Earth  I      Mars      I     Jupiter    I    Saturn    I      Georgian 
87,9692     I  2246.176      |  365.2564       |  686.9785    |    4332.514    |  1079.275   |          30456.07 

Relative  mean  distances  from  the  Sun. 

38710  |    72333  |   100000   |    152369  |    520096  |    954006  \     1908580 

From  these  numbers  we  deduce,  that  if  the  Sun's  horizontal 
fiarallax  be  10",  t he  real  mean  distances   of  the  planets 
from  the  Sun  in  English  miles,  are 

[31,742,200  |  59,313,060  |  82,000,000  |  124,942,680  |  426,478,720  |  782,284,920  |  1,565,035,600 

But  if  the  Sun'.?  parallax  be  1 1""  their  distances  are  no  more  than 

29,032,500  I  54,238,570  '|  75,000,000  |  114,276,750  1  390,034,500  |  715,504,500  |  1,431,435,000 

Errors  in  distance  arising  from  the  mistake  of  \"  in  the  Sun's 
parallax. 

2,709,700  |      5,074,490  \  7,000,000  |  10,665,830  |      35,444,220  |    66,780,420  |        133,600,600 

But,  from  the  late  transit  of  Venus,  A.   D.  1761,  the   Sun's 

fiarallax  appears  to  be  only  %f  -£$-5  i  and  according   to  that, 

their  real  distances  in  miles  are 

36,841,468  I  68,891,486  |  95,173,127  |  145,014,148  |  494,990,976  |  907,956,130  |  1,816,455,526 

And  their  diameters  in  wiles,  are, 

3100 1      9360  |     7970  |      5150  |    94,1000  |    77,990  |      35,226 

195.  These  numbers  shew,  that  although  we 
have  the  relative  distances  of  the  planets  from  the 
Sun,  to  the  greatest  nicety,  yet  the  best  observers 
could  not  ascertain  their  true  distances  until  the  late 
long-wished-for  transit  appeared,  in  1761,  which  we 
must  confess  was  embarrassed  with  several  difficul- 
ties.    But  another  transit  of  Venus  over  the  Sun, 
has  now  been  observed,  on  the  third  of  June.  1769, 
much  better  suited  to  the  resolution  of  this  great 
problem  than  that  in  1761  was;  and  the  result  of 
the  observations  does  not  differ  materially  from  the 
result  of  those  in  1761.    No  other  transit  will  hap- 
pen till  the  year  1874. 

196.  The  Earth's  axis  produced  to  the  stars,  be- 
ing carried  parallel*  to  itself  during  the  Earth's  an- 
nual revolution,  describes  a  circle  in  the  sphere  of 

why  the  the  fixed  stars  equal  to  the  orbit  of  the  Earth.  But 
°oiestial  ^*s  ork"lt'  though  very  large,  would  seem  no  big- 
seem  to  ger  than  a  point,  if  it  were  viewed  from  the  stars ; 

keep  still 

in  *  By  this  is  meant,  that  if  a  line  be  supposed  to  be  drawn  paral- 

lel to  the  Earth's  axis  in  any  part  of  its  orbit,  the  axis  keeps  parallel 
to  that  line  in  every  other  part  of  its  orbit :  as  in  fig.  I.  of  plate  V. 
where  abed  efgh  represents  the  Earth's  orbit  in  an  oblique  view, 
and  N$  the  Earth's  axis  keeping  always  parallel  to  the  line  M A, 


The  amazing  velocity  of  Light.  139 


and  consequently  the  circle  described  in  the  sphere  th<r  sarn« 

i  r-1        T?      .1  i     -rPOintsof 

of  the  stars  by  the  axis  ot  the  Earth,  produced,  ifthehea- 
viewed  from  the  earth,  must  appear  but  as  a  point  ;  vens,  not- 
that  is,  its  diameter  appears  too  little  to  be  measur-  ^the" 
ed  by  observation:  for  Dr.  BRADLEY  has  assured  Earth's 
us,  that  if  it  had  amounted  to  a  single  second,  or  two  ™°^Jnthe 
at  most,  he  should  have  perceived  it  in  the  number  sun. 
of  observations  he  has  made,  especially  upon  T  Dra- 
conis;  and  that  it  seemed  to  him  very  probable  that 
the  annual  parallax  of  this  star  is  not  so  great  as  a 
single  second  :  and  consequently,  that  it   is  above 
400  thousand  times  farther  from  us  than  the  Sun. 
Hence  the  celestial  poles  seem  to  continue  in  the 
same  points  of  the  heavens  throughout  the  year; 
which  by  no  means  disproves  the  Earth's  annual 
motion,  but  plainly  proves  the  distance  of  the  stars 
to  be  exceeding  great, 

197.  The  small  apparent  motion  of  the  stars,  J  113, 
discovered  by  that  great  astronomer,  he  found  to  be 
no  ways  owing  to  their  annual  parallax,  (for  it  came 
out  contrary  thereto,)  but  to  the  aberration  of  their 
light,  which  can  result  from  no  known  cause,  be- 
sides that  of  the  Earth's  annual  motion  ;  and  as  it 
agrees  so  exactly  therewith,  it  proves  beyond  dispute, 
that  the  Earth  has  such  a  motion  ;  for  this  aberration 
completes  all  its  various  phenomena  every  year  ;  and  The  ama- 
proves  that  the  velocity  of  star-light  is  such  as  car-  zjn£  Do- 
ries it  through  a  space  equal  to  the  Sun's  distance 
from  us  in  8  minutes  13  seconds  of  time.  Hence 
the  velocity  of  light  is  *10  thousand  2  10  times  as  great 
as  the  Earth's  vetocity  in  its  orbit  ;  which  velocity, 
f  from  what  we  know  already  of  the  Earth's  distance 
from  the  Sun)  may  be  asserted  to  be  at  least  between 
57  and  58  thousand  miles  every  hour  :  and  suppos- 
ing it  to  be  58000,  this  number  multiplied  by 
10210,  gives  592  million  180  thousand  miles  for 
the  hourly  motion  of  light  :  which  last  number  divi- 
ded by  5600,  the  number  of  seconds  in  an  hour, 

*  SMITH'S  Optic's  §  1197. 


140  Of  the  different  Seasons. 

Plate  ir.  shews  that  light  flies  at  the  rate  of  more  than  164 
thousand  miles  every  second  of  time,  or  swing  of  a 
common  clock  pendulum. 

CHAP.  X. 

The  Circles  of  the  Globe  described.  The  different 
Lengths  of  Days  and  Nights,  and  the  Vicissitudes 
of  the  Seasons y  explained.  The  explanation  oj* 
the  Phenomena  of  Saturn* s  Ring  concluded.  (See 
§  81  and  82. 

circi    of  198    T^?  t^ie  reac^er  be  hitherto  unacquainted  with 
the° e  '  JL  tne  principal  circles  of  the  globe,  he  should 

sphere,     now  learn  to  know  them ;  which  he  may  do  suffi- 
ciently for  his  present  purpose  in  a  quarter  of  an 
hour,  if  he  sets  the  ball  of  a  terrestrial  globe  before 
Fi£-  H.     him,  or  looks  at  the  figure  of  it,  wherein  these  cir- 

E  uator    C^es  are  ^rawn  an^  name^'     The  equator  is  that 
tropics*'   great  circle  which  divides  the  northern  half  of  the 
polar  cir-  Earth  from  the  southern.    The  tropics  are  lesser 
poles and  circles  parallel  to  the  equator ;  each  of  them  being 
231  degrees  from  it;  a  degree  in  this  sense  being 
the  360th  part  of  any  great  circle ;  or  that  which  di- 
vides the  Earth  into  two  equal  parts.     The  tropic  of 
Cancer  lies  on  the  north  side  of  the  equator,  and  the 
tropic  of  Capricorn  on  the  south.     The  Arctic  cir- 
Flg'  IL    cle  has  the  North  pole  for  its  centre,  and  is  just  as 
far  from  it  as  the  tropics  are  from  the  equator ;  and 
the  Ant  arctic  cir  cle,  (hid  by  the  supposed  convexity 
of  the  figure)  is  just  as  far  from  the  southpole  every 
way  round   it.     These   poles  are   the  very  north 
and  south  points  of  the  globe :   and  all  other  places 
are  denominated  northward  or  southward^  according 
to  the  side  of  the  equator  they  lie  on,  and  the  pole  to 
Earth's     which  they  are  nearest.  The  Earth* s  axis  is  a  straight 
a**5-        line  passing  through  the  centre  of  the  Earth,  perpen- 
dicular to  the  equator,  and  terminating  in  the  poles 
at  its  surface.     This,  in  the  real  Earth  and  planets, 
is  only  an  imaginary  line  \  but  in  artificial  globes  or 
planets  it  is  a  wire  by  which  they  are  supported,  and 


Of  the  different  Seasons.  141 

turned  round  in  Orreries,  or  such  like  machines,  by  plate  lv- 
wheel- work.    The  circles  12.    1.  2.  3.  4.  &c.  arc 
meridians  to  all  places  they  pass  through;  and  weMeridi- 
must  suppose  thousands  more  to  be  drawn,  because  ans* 
every  place,  that  is  ever  so  little  to  the  east  or  west 
of  any  other  place,  has  a  different  meridian  from  that 
other  place.     All  the  meridians  meet  in  the  poles ; 
and  whenever  the  Sun's  centre  is  passing  over  any- 
meridian  in  his  apparent  motion  round  the  Earth,  it 
is  mid-day  or  noon  to  all  places  on  that  meridian. 

199.  The  broad  space  lying  between  the  tropics, 
like  a  girdle  surrounding  the  globe,  is  called  the  tor- 
rid zone,  of  which  the  equator  is  in  the  middle  all201 
round.     The  space  between  the  tropic  of  Cancer 
and  Arctic  circle,  is  called  the  north  temperate  zone  ; 
that  between  the  tropic  of  Capricorn  and  the  An- 
tarctic circle,  the  south  temperate  zone;  and  the 
two  circular  spaces  bounded  by  the  polar  circles,  are 
the  two  frigid  zones;  denominated  north  or  south, 
from  that  pole  which  is  in  the  centre  of  the  one  or 
the  other  of  them. 

200.  Having  acquired  this  easy  branch  of  know- 
ledge, the  learner  may  proceed  to  make  the  follow- 
ing experiment  \vith  his  terrestrial  ball ;  which  will 
give  him  a  plain  idea  of  the  diurnal  and  annual  mo- 
tions of  the  Earth,  together  with  the  different  lengths 
of  days,  nights,  and  all  the  beautiful  variety  of  sea- 
sons, depending  on  those  motions. 

Take  about  seven  feet  of  strong  wire,  and  bend  Fig.  in. 
it  into  a  circular  form,  as  abed,  which  being  viewed  ^gxp'e- 
obliquely,  appears  elliptical,  as  in  the  figure.    Place  riment 
a  lighted  candle  on  a  table,  and  having  fixed  one  end*^^|r 
of  a  silk  thread  K,  to  the  north  pole  of  a  small  terres-  ent 
trial  plobe  H,  about  three  inches  diameter,  cause  lengths  o 

i  °  ,  ,     ,  .  ,  ,        .  days  and 

another  person  to  hold  the  wire-circle,  so  that  it  may  ni^ts, 
be  parallel  to  the  table,  and  as  high  as  the  flame  of  and  the 
the  candle  /,  which  should  be  in  or  near 


142  Of  the  different  Seasons, 

centre.  Then,  having  twisted  the  thread  as  to 
ward  the  left  hand,  that  by  untwisting  it  may 
turn  the  globe  round  eastward,  or  contrary  to 
the  way  that  the  hands  of  a  watch  move,  hang 
the  globe  by  the  thread  within  this  circle,  al- 
most contiguous  to  it ;  and  as  the  thread  untwists, 
the  globe  (which  is  enlightened  half  round  by  the 
candle,  as  the  Earth  is  by  the  Sun)  will  turn  round 
its  axis,  and  the  different  places  upon  it  will  be  car- 
ried through  the  light  and  dark  hemispheres,  and 
have  the  appearance  of  a  regular  succession  of  days 
and  nights,  as  our  Earth  has  in  reality  by  such  a 
motion.  As  the  globe  turns,  move  your  hand  slow- 
ly, so  as  to  carry  the  globe  round  the  candle  accor- 
ding to  the  order  of  the  letters  abed,  keeping  its 
centre  even  with  the  wire-circle  ;  and  you  will  per- 
ceive, that  the  candle,  being  still  perpendicular  to 
the  equator,  will  enlighten  the  globe  from  pole  to 
pole  in  its  whole  motion  round  the  circle;  and  that 
every  place  on  the  globe  goes  equally  through  the 
light  and  the  dark,  as  it  turns  round  by  the  untwist- 
ing of  the  thread,  and  therefore  has  a  perpetual 
equinox.  The  globe  thus  turning  round  represents 
the  Earth  turning  round  its  axis ;  and  the  motion  of 
the  globe  round  the  candle  represents  the  Earth's 
annual  motion  round  the  Sun,  and  shews,  that  if 
the  Earth's  orbit  had  no  inclination  to  its  axis,  all 
the  days  and  nights  of  the  year  would  be  equally 
long,  and  there  would  be  no  different  seasons.  But 
now,  desire  the  person  who  holds  the  wire  to  hold 
it  obliquely  in  the  position  ABCD,  raising  the  side 
93  just  as  much  as  he  depresses  the  side  >5 ,  that 
the  flame  may  be  still  in  the  plane  of  the  circle ; 
and  twisting  the  thread  as  before,  that  the  globe 
may  turn  round  its  axis  the  same  way  as  you 
carry  it  round  the  candle,  that  is,  from  west  to 
east,  let  the  globe  down  into  the  lowermost  part 
of  the  wire  circle  at  VJ ,  and  if  the  circle  be  pro- 
perly inclined,  the  candle  will  shine  perpendicular 


OftJte  different  Seasons.  143 

cularly  on  the  tropic  of  Cancer,  and  tlieffigid  zone,  Summer 
lying  within  the  Arctic  or  north  polar  circle,  will  be solstice- 
all  in  the  light,  as  in  the  figure ;  and  will  keep  in  the 
light,  let  the  globe  turn  round  its  axis  ever  so  often. 
From  the  equator  to  the  north  polar  circle  all  the 
places  have  longer  days  and  shorter  nights ;  but 
from  the  equator  to  the  south  polar  circle  just  the 
reverse.  The  Sun  does  not  set  to  any  part  of  the 
north  frigid  zone,  as  shewn  by  the  candle's  shining 
on  it,  so  that  the  motion  of  the  globe  can  carry  no 
place  of  that  zone  into  the  dark :  and  at  the  same 
time  the  south  frigid  zone  is  involved  in  darkness, 
and  the  turning  of  the  globe  brings  none  of  its  places 
into  the  light.  If  the  Karth  were  to  continue  in  the 
like  part  of  its  orbit,  the  Sun  would  never  set  to  the 
inhabitants  of  the  north  frigid  zone,  nor  rise  to  those 
of  the  south.  At  the  equator  it  would  be  alvyays 
equal  day  and  night;  and  as  places  are  gradually 
more  and  more  distant  from  the  equator,  toward  the 
Arctic  circle,  they  would  have  longer  days  and 
shorter  nights ;  while  those  on  the  south  side  of  the 
equator  would  have  their  nights  longer  than  their 
days.  In  this  case  there  wrould  be  continual  sum- 
mer on  the  north  side  of  the  equator,  and  continual 
winter  on  the  south  side  of  it. 

But  as  the  globe  turns  round  its  axis,  move  your 
hand  slowly  forward,  so  as  to  carry  the  globe  from 
//toward  E,  and  the  boundary  of  light  and  dark- 
ness will  approach  toward  the  north  pole,  and  recede 
from  the  south  pole;  the  northern  places  will  go 
through  less  and  less  of  the  light,  and  the  southern 
places  through  more  and  more  of  it ;  shewing  how 
the  northern  days  decrease  in  length,  and  the 
southern  days  increase,  while  the  globe  proceeds 
from  H  to  E.  When  the  globe  is  at  E,  it  is  at  a 
mean  state  between  the  lowest  and  highest  parts  of  Autumnal 
its  orbit ;  the  candle  is  directly  over  the  equator,  the  equinox. 
boundary  of  light  and  darkness  just  reaches  to  both 

T 


144  Of  the  different  Seasons. 

the  poles,  and  all  places  on  the  globe  go  equally 
through  the  light  and  dark  hemispheres,  shewing 
that  the  days  and  nights  are  then  equal  at  ail  places 
of  the  Earth,  the  poles  only  excepted ;  for  the  Sun 
is  then  setting  to  the  north  pole,  and  rising  to  the 
south  pole. 

Continue  moving  the  globe  forward,  and  as  it 
goes  through  the  quarter  A,  the  north  pole  recedes 
still  farther  into  the  dark  hemisphere,  and  the  south 
pole  advances  more   into  the   light,   as  the  globe 
comes  nearer  to  25 :  and  when  it  comes  there  at  Ft 
winter     the  candle  is  directly  over  the  tropic  of  Capricorn, 
solstice.    the  days  are  at  tne  shortest,  and  nights  at  the  longest, 
in  the  northern  hemisphere,  all  the  way  from  the 
.  equator  to  the  Arctic  circle ;  and  the  reverse  in  the 
southern  hemisphere  from  the  equator  to  the  Antarc- 
tic circle  ;  within  which  circles  it  is  dark  to  the  north 
frigid  zone,  and  light  to  the  south. 

Continue  both  motions,  and  as  the  globe  moves 
through  the  quarter  J3,  the  north  pole  advances  to- 
ward the  light,  and  the  south  pole  toward  the  dark ; 
the  days  lengthen  in  the  northern  hemisphere,  and 
shorten  in  the  southern ;  and  when  the  globe  comes 
to  G,  the  candle  will  be  again  over  the  equator,  (as 
Vernal  when  the  globe  was  at  E,)  and  the  days  and  nights 
w-j|  agajn  be  equai  as  formerly ;  and  the  north  pole 
will  be  just  coming  into  the  light,  the  south  pole  go- 
ing out  of  it. 

Thus  we  see  the  reason  why  the  days  lengthen 
and  shorten  from  the  equator  to  the  polar  circles 
every  year ;  why  there  is  sometimes  no  day  or  night 
for  many  turnings  of  the  Earth,  within  the  polar  cir- 
cles ;  why  there  is  but  one  day  and  one  night  in  the 
whole  year  at  the  poles ;  and  why  the  days  and  nights 
are  equally  long  all  the  year  round  at  the  equator, 
•which  is  always  equally  cut  by  the  circle  bounding 
light  and  darkness. 


Of  the  different  Seasons.  145 

201.  The  inclination  of  an  axis  or  orbit  is  merely  Remark, 
relative,  because  we  compare  it  with  some  other 
axis  or  orbit  which  we  consider  as  not  inclined  at  all. 
Thus,  our  horizon  being  level  to  us,  whatever  place 
of  the  Earth  we  are  upon,  we  consider  it  as  having  Pjatc  jj^ 
no  inclination  ;  and  yet,  if  we  travel  90  degrees  from  Fig.  in. 
that  place,  we  shall  then  have  a  horizon  perpendicu- 
lar to  the  former,  but  it  will  still  be  level  to  us. 
And  if  this  book  be  held  so  that  the  *  circle  ABCD 
be  parallel  to  the  horizon,  both  the  circle  abed,  and 
the  thread  or  axis  K,  will  be  inclined  to  it.  But  if 
the  book  or  plate  be  held  so  that  the  thread  be  per- 
pendicular to  the  horizon,  then  the  Q?\y\lABCD  will 
be  inclined  to  the  thread,  and  the  orbit  abed  perpen- 
dicular to  it,  and  parallel  to  the  horizon.  We  gene- 
rally consider  the  Earth's  annual  orbit  as  having  no 
inclination,  and  the  orbits  of  all  the  other  planets  as 
inclined  to  it,  $  20. 

202:  Let  us  now  take  a  view  of  the  Earth  in  its 
annual  course  round  the  Sun,  considering  its  orbit 
as  having  no  inclination,  and  its  axis  as  inclining  23  J 
degrees  from  a  line  perpendicular  to  the  plane  of  its 
orbit,  and  keeping  the  same  oblique  direction  in  all 
parts  of  its  annual  course ;  or,  as  commonly  termed, 
keeping  always  parallel  to  itself,  §  196. 

Let  #,  b,  c,  d,  e,,f,g,  h,  be  the  Earth  in  eight  dif-  Plate  r. 
ferent  parts  of  its  orbit,  equidistant  from  one  another:  Fiff- L 
JV  s  its  axis,  JVits  north  pole,  s  its  south  pole,  and 
S  the  Sun  nearly  in  the  centre  of  the  Earth's  orbit, 
§  18.     As  the  Earth  goes  round  the  Sun  according 

*  All  circles  appear  elliptical  in  an  oblique  view,  as  is  evident  by 
looking  obliquely  at  the  rim  of  a  bason.  For  the  true  figure  of  a  cir- 
cle can  only  be  seen  when  the  eye  is  directly  over  its  centre.  The 
more  obliquely  it  is  viewed,  the  more  elliptical  it  appears,  until  the 
eye  be  in  the  same  plane  with  it,  and  then  it  appears  life  a  straight 
linr. 


146  Of  the  different  Seasons. 

Plate  v.  to  the  order,  of  the  letters  abed,  &c.  its  axis  A"^  keeps 
the  same  obliquity,  and  is  still  parallel  to  the  line 
A  concise  M  N  s.  When  the  Earth  is  at  a,  its  north  pole  in- 
Ieasonsthe  c^nes  toward  the  Sun  S,  and  brings  all  the  northern 
places  more  into  the  light  than  at  any  other  time  of 
the  year.  But  when  the  Earth  is  at  e  in  the  opposite 
time  of  the  year,  the  north  pole  declines  from  the 
Sun,  which  occasions  the  northern  places  to  be  more 
in  the  dark  than  in  the  light ;  and  the  reverse  at  the 
southern  places,  as  is  evident  by  the  figure,  which 
I  have  taken  from  Dr.  LONG'S  Astronomy.  When 
the  Earth  is  either  at  c  or  g,  its  axis  inclines  not 
cither  to  or  from  the  Sun,  but  lies  side  wise  to  him ; 
and  then  the  poles  are  in  the  boundary  of  light  and 
darkness;  and  the  Sun,  being  directly  over  the  equa- 
tor, makes  equal  day  and  night  at  all  places.  When 
the  Earth  is  at  b,  it  is  half-way  between  the  Summer 
solstice  and  harvest  equinox ;  when  it  is  at  d,  it  is 
half  way  from  the  harvest  equinox  to  the  winter  sol- 
stice ;  at  s,  half  way  from  the  winter  solstice  to  the 
spring  equinox  ;  and  at  /z,  half  way  from  the  spring 
equinox  to  the  summer  solstice. 

Fig.  II.          203.  From  this  oblique  view  of  the  Earth's  orbit, 

let  us  suppose  ourselves  to  be  raised  far  above  it, 

and  placed  just  over  its  centre  S,  looking  down  upon 

it  from  its  north  pole ;  and  as  the  Earth's  orbit  differs 

but  very  little  from  a  circle,  we  shall  have  its  figure  in 

such  a  view  represented  by  the  circle  ABCDEFGH. 

Let  us  suppose  this  circle  to  be  divided  into  12  equal 

parts,  called  sigm,  having  their  names  affixed  to  them: 

and  each  sign  into  30  equal  parts,  called  degrees, 

The  sea-   numbered  10,  20,  30,  as  in  the  outermost  circle  of 

sons          the  figure,  which  represents  the  great  ecliptic  in  the 

another11   heavens.     The  Earth  is   shewn  in  eight  different 

view  of     positions  in  this  circle :  and  in  each  position  M  is  the 

Indfts^1  e(luator>  ^  the  tropic  of  Cancer,  the  dotted  circle 

orbit. 


Of  the  different  Seasons.  147 

the  parallel  of  London,  U  the  Arctic  or  north  polar 
circle,  and  Pthe  north  pole,  where  all  the  meridians 
or  hour-circles  meet,  £  198.  As  the  Earth  goes 
round  the  Sun,  the  north  pole  keeps  constantly  to- 
ward one  part  of  the  heavens,  as  it  does  in  the  figure 
toward  the  right-hand  side  of  the  plate. 

When  the  Earth  is  at  the  beginning  of  Libra, 
namely,  on  the  20th  of  March  in  tiiis  figure  (as  at  g 
in  Fig.  I.)  the  Sun  S,  as  seen  from  the  Earth,  ap- 
pears at  the  beginning  of  Aries,  in  the  opposite  part 
of  the  heavens*,  the  north  pole  is  just  coming  into 
the  light,  and  the  Sun  is  vertical  to  the  equator;  vernal 
which,  together  with  the  tropic  of  Cancer,  parallel  equinox, 
of  London,  and  Arctic  circle,  are  all  equally  cut  by 
the  circle  bounding  light  and  darkness,  coinciding 
with  the  six  o'clock  hour-circle,  and  therefore  the 
days  and  nights  are  equally  long  at  all  places  :  for 
every  part  of  the  meridians  JETjLd  comes  into  the 
light  at  six  in  the  morning,  and  revolving  with  the 
Earth  according  to  the  order  of  the  hour-letters  goes 
into  the  dark  at  six  in  the  evening.  There  are  24 
meridians,  or  hour-circles  drawn  on  the  Earth  in  this 
figure,  to  shew  the  time  of  sun-rising  and  setting  at 
different  seasons  of  the  year. 

As  the  Earth  moves  in  the  ecliptic  according  to 
the  order  of  the  letters  ABCD,  &c.  through  the 
signs,  Libra,  Scorpio,  and  Sagittarius,-  the  north 
pole  P  comes  more  and  more  into  the  light ;  the 
days  increase  as  the  nights  decrease  in  length  at  all 
places  north  of  the  equator./®;  which  is  plain  by 
viewing  the  Earth  at  b  on  the  5th  of  May,  when  it 
is  in  the  15th  degree  of  Scorpio  f,  and  the  Sun,  as 

*  Here  \ve  nmst  suppose  the  Sun  to  be  no  bigger  than  an  ordinary 
point  (•  s.)  because  he  only  covers  a  circle  half  a  degree  in  diameter 
in  the  heavens;  whereas  in  the  figure  he  hides  a  -whole  sign  at  once 
from  the  Earth. 

t  Here  we  must  suppose  the  Earth  to  be  a  much  smaller  point  than 
that  in  the  preceding  note  marked  for  the  Sun. 


148  Of  the  different  Seasons. 

Plate  r.     seen  from  the  Earth,  appears  in  the  15th  degree  of 
Taurus.     For  then,  the  tropic  of  Cancer  T  is  in  the 
Fig.  ii.      light  from  a  little  after  five  in  the  morning  till  almost 
_ seven  in  the  evening;   the  parallel  of  London  from 
half  an  hour  past  four  till  half  an  hour  past  seven ; 
the  polar  circle  U  from  three  till  nine ;  and  a  large 
track  round  the  north  pole  P  has  day  all  the  24 
hours,  for  many  rotations  of  the  Earth  on  its  axis. 

When  the  Earth  comes  to  c,  at  the  beginning  of 
Capricorn,  and  the  Sun,  as  seen  from  the  Earth  ap- 
pears at  the  beginning  of  Cancer,  on  the  21st  of 
June,  as  in  this  figure,  it  is  in  the  position  a  in  Fig. 
I;  and  its  north  pole  inclines  toward  the  Sun,  so  as 
to  bring  all  the  north  frigid  zone  into  the  light,  and 
the  northern  parallels  of  latitude  more  into  the  light 
than  the  dark  from  the  equator  to  the  polar  circle ; 
and  the  more  so  as  they  are  farther  from  the  equator. 
The  tropic  of  Cancer  is  in  the  light  from  five  in  die 
morning  till  seven  at  night ;  the  parallel  of  London 
from  a  quarter  before  four  till  a  quarter  after  eight ; 
and  the  polar  circle  just  touches  the  dark,  so  that  the 
Summer  Sun  has  only  the  lower  half  of  his  disc  hid  from  the 
solstice,  inhabitants* on  that  circle  for  a  few  minutes  about 
midnight,  supposing  no  inequalities  in  the  horizon, 
and  no  refraction. 

A  bare  view  of  the  figure  is  enough  to  shew,  that 
as  the  Earth  advances  from  Capricorn  toward  Aries, 
and  the  Sun  appears  to  move  from  Cancer  toward 
Libra,  the  north  pole  advances  toward  the  dark, 
which  causes  the  days  to  decrease,  and  the  nights  to 
Autumnal  increase  in  length,  till  the  Earth  comes  to  the  begin- 
Equinox.  ning  of  A  rics,  and  then  they  are  equal  as  before ;  for 
the  boundary  of  light  and  darkness  cuts  the  equator 
and  all  its  parallels  equally,  or  in  halves.  The  north 
pole  then  goes  into  the  dark,  and  continues  in  it  until 
the  Earth  goes  half  way  round  its  orbit ;  or,  from 
the  23d  of  *  September  till  the  20th  of  March.  In  the 


Of  the  different  Seasons.  149 

middle,  between  these  times,  viz.  on  the  22d  ,of Winter 
December,  the  north  pole  is  as  far  as  it  can  be  in  the solstlce* 
dark,  which  is  23£  degrees,  equal  to  the  inclination 
of  the  Earth's  axis  from  a  perpendicular  to  its  orbit: 
and  then  the  northern  parallels  are  as  much  in  the 
dark  as  they  were  in  the  light  on  the  21st  of  June; 
the  winter  nights  being  as  long  as  the  summer  days, 
and  the  winter  days  as  short  as  the  summer  nights. 
It  is  needless  to  enlarge  farther  on  this  subject,  as 
we  shall  have  occasion  to  mention  the  seasons  again 
in  describing  the  Orrery >  &  397.  Only  this  must  be 
noted,  that  whatever  has  been  said  of  the  northern 
hemisphere,  the  contrary  must  be  understood  of  the 
southern ;  for  on  different  sides'  of  the  equator  the 
seasons  are  contrary ;  because,  when  the  northern 
hemisphere  inclines  toward  the  Sun,  the  southern 
declines  from  him. 

204.  As  Saturn  goes  round  the  Sun,  his  oblique- The  phe- 
ly-posited  ring,  like  our  Earth's  axis,  keeps  parallel  ™ s 
to  itself,  and  is  therefore  turned  edgewise  to  the  Sun  ring7 
twice  in  a  Saturnian  year;  which  is  almost  as  long 
as  30  of  our  years,  §81.  But  the  ring,  though  con- 
siderably broad,  is  too  thin  to  be  seen  by  us  when  it 
is  turned  edgewise  to  the  Sun,  at  which  time  it  is 
also  edgewise  to  the  Earth ;  and  therefore  it  disap- 
pears once  in  every  fifteen  years  to  us.  As  the 
Sun  shines  half  a  year  together  on  the  north 
pole  of  our  Earth,  then  disappears  to  it,  and  shines 
as  long  on  the  south  pole;  so,  during  one  half 
of  Saturn's  year,  the  Sun  shines  on  the  north  side 
of  his  ring,  then  disappears  to  it,  and  shines  as  long 
on  the  south  side.  When  the  Earth's  axis  inclines 
neither  to  nor  from  the  Sun,  but  is  side  wise  to  him, 
he  then  ceases  to  shine  on  one  pole,  and  begins  to 
enlighten  the  other;  and  when  Saturn's  ring  inclines 
neither  to  nor  from  the  Sun,  but  is  edgewise  to  him, 


150  Of  the  different  Seasons. 

Plate  v.    he  ceases  to  shine  on  the  one  side  of  it,  and  begins 
to  shine  upon  the  other. 

Fiff.  in.  Let  S  be  the  Sun,  ABCDEFGII  Saturn's  orbit, 
and  IKLMNO  the  Earth's  orbit.  Bqth  Saturn  and 
the  Earth  move  according  to  the  order  of  the  letters : 
v.  hen  Saturn  is  at  A  his  ring  is  turned  edgewise  to 
the  Sun  S,  and  he  is  then  seen  from  the  Earth  as  if 
he  had  lost  his  ring,  let  the  Earth  be  in  any  part  of 
its  orbit  whatever,  except  between  N  and  O;  for 
while  it  describes  that  space,  Saturn  is  apparently  so 
near  the  Sun  as  to  be  hid  in  his  beams.  As  Saturn 
goes  from  A  to  C,  his  ring  appears  more  and  more 
open  to  the  Earth  :  at  Cthe  ring  appears  most  open  of 
all;  and  seems  to  gro\v  narrower  and  narrower,  as  Sa- 
turn goes  from  CtoE,  and  when  he  comes  to  E,  the 
ring  is  agnin  turned  edgewise  both  to  the  Sun  and 
Earth ;  and  as  neither  of  its  sides  are  illuminated,  it 
is  invisible  to  us,  because  its  edge  is  too  thin  to  be 
perceptible ;  and  Saturn  appears  again  as  if  he  had 
lost  his  ring.  But  as  he  goes  from  E  to  G,  his  ring 
opens  more  and  more  to  our  view  on  the  under  side ; 
and  seems  just  as  open  at  G  as  it  was  at  C;  and  may 
be  seen  in  the  night  time  from  the  Eartli  in  any  part 
of  its  orbit,  except  about  J/,  when  the  Sun  hides 
the  planet  from  our  view.  As  Saturn  goes  from  G 
to  A,  his  ring  turns  more  and  more  edgewise  to  us, 
and  therefore  it  seems  to  grow  narrower  and  nar- 
rower; and  at  A,  it  disappears  as  before.  Hence,  while 
Saturn  goes  from  A  to  E,  the  Sun  shines  on  the  upper 
side  of  his  ring,  and  the  under  side  is  dark ;  and 
while  he  goes  from  E  to  A,  the  Sun  shines  on  the 
under  side  of  his  ring,  and  the  upper  side  is  dark. 

It  may  perhaps  be  imagined  that  this  article 
might  have  been  placed  more  properly  after  $  81, 
than  here;  but  when  the  candid  reader  considers 

Fi£.i.  and  that  all  the   various  phenomena  of  Saturn's  ring 

In-         depend  upon  a  cause  similar  to  that  of  our  Earth's 


Of  the  different  Seasons.  151 

seasons,  he  will  readily  allow  that  they  are  best  ex- Piate  VL 
plained  together  ;  and  that  the  two  figures  serve  to 
illustrate  each  other. 

205.  The  Earth's  orbit  being  elliptical,  and  the  The  Earth 
Sun  keeping  constantly  in  its  lower  focus,  which  is  stmin ^ 
1,377,000  miles  from  the  middle  point  of  the  longer  winter 
axis,  the  Earth  comes  twice  so  much,  0^2,754,000^^ 
miles,  nearer  the  Sun  at  one  time  of  the  year  than 

at  another :  for  the  Sun  appearing  to  us  under  a 
larger  angle  in  winter  than  in  summer,  proves  that 
the  Earth  is  nearest  the  Sun  in  winter  (see  the 
Note  on  Article  185^.  But  here  this  natural  ques-  why th« 
tion  will  arise :  Why  have  we  not  the  hottest  weather  ^Jit* IS 
when  the  Earth  is  nearest  the  Sun  ?  In  answer  it  when  the 
must  be  observed,  that  the  eccentricity  of  the  Earth?s  ^*^£ 
orbit,  or  1,377,000  miles,  bears  no  greater  proper- the  Sun. 
tion  to  the  Earth's  mean  distance  from  the  Sun, 
than  17  does  to  1000;  and  therefore  this  small  differ- 
ence of  distance  cannot  occasion  any  sensible  differ- 
ence of  heat  or  cold.  But  the  principal  cause  of  this 
difference  is,  that  in  winter  the  Sun's  rays  fall  so  ob- 
liquely upon  us,  that  any  given  number  of  them  is 
spread  over  a  much  greater  portion  of  the  Earth's 
surface  where  we  live,  and  therefore  each  point  must 
then  have  fewer  rays  than  in  summer.  Moreover, 
there  comes  a  greater  degree  of  cold  in  the  long 
winter  nights,  than  there  can  return  of  heat  in  so  short 
days ;  and  on  both  these  accounts  the  cold  must  in- 
crease. But  in  summer  the  Sun's  rays  fall  more 
perpendicularly  upon  us,  and  therefore  come  with 
greater  force,  and  in  greater  numbers  on  the  same 
place  ;  and  by  their  long  continuance,  a  much  great- 
er degree  of  heat  is  imparted  by  day  than  can  fly  off 
by  night. 

206.  That  a  greater  number  of 'rays  fall  on  the 
same  place,  when  they  come  perpendicularly,  than 
when  they  come  obliquely  on  it,  will  appear  by  the 
figure.     For,  let  AB  be  a  certain  number  of  the  Fig.  it 
Sun's  'rays  falling  on  CD  (which  let  us  suppose  to 


152  The  Method  of  finding  the  Longitude. 

be  London )  on  the  21st  of  June:  but,  on  the  22d 
of  December,  the  line  CD,  or  London,  has  the  ob- 
lique position  CD  to  the  same  rays ;  and  therefore 
scarce  a  third  part  of  them  falls  upon  it,  or  only  those 
between  *4ande>;  all  the  rest,  cB,  being  expended 
on  the  space  d  P,  which  is  more  than  double 
the  length  of  CD  or  Cd.  Besides,  those  parts 
which  are  once  heated,  retain  the  heat  for  some 
time ;  which,  with  the  additional  heat  daily  impart- 
ed, makes  it  continue  to  increase,  though  the  Sun 
declines  toward  the  south ;  and  this  is  the  reason 
why  July  is  hotter  than  June,  although  the  Sun  has 
withdrawn  from  the  summer  tropic ;  as  we  find  it  is 
generally  hotter  at  three  in  the  afternoon,  when  the 
Sun  has  gone  toward  the  west,  than  at  noon  when 
he  is  on  the  meridian.  Likewise,  those  places  which 
are  well  cooled  require  time  to  be  heated  again ;  for 
the  Sun's  rays  do  not  heat  even  the  surface  of  any 
body  till  they  have  been  some  time  upon  it.  And 
therefore  we  find  January,  for  the  most  part,  colder 
than  December,  although  the  Sun  has  withdrawn 
from  the  winter  tropic,  and  begins  to  dart  his  beams 
more  perpendicularly  upon  us,  when  we  have  the 
position  CF.  An  iron  bar  is  not  heated  immediate- 
ly upon  being  put  into  the  fire,  nor  grows  cold  till 
some  time  after  it  has  been  taken  out. 

CHAP.  XL 

The  Method  of  finding  the  Longitude  by  the  Eclips- 
es of  Jupiter'1  s  Satellites :  the  amazing  Velocity  of 
Light  demonstrated  by  these  Eclipses. 

OA-  /^  EOGRAPHERS  arbitrarily  choose  to 

Virstihe-  207.  I    -w        n    a  -j-  r  111 

ridian,  \J  call  the  meridian   of  some   remarkable 

and  ion-    place  the  first  meridian.     There  they  begin  their 

places,0    reckoning ;  and  just  so  many  degrees  and  minutes 

what.       as  any  other  place  is  to  the  eastward  or  westward  of 

that  meridian,  so  much  east  or  west  longitude  they 

say  it  has.     A  degree  is  the  360th  part  of  a  circle, 


p 

The  Method  of  finding  the  Longitude.  153 

be  it  great  or  small,  and  a  minute  the  60th  part  of  a pla* '  v- 
degree.  The  English  geographers  reckon  the  longi- 
tude from  the  meridian  of  the  Royal  Observatory  at 
Greenwich,   and  the  French  from  the  meridian  of 
Paris. 

208.  If  we  imagine  two   great   circles,  one  ofFJff-IL 
which  is  the  meridian  of  any  given  place,  to  inter-  Hour  cir- 
sect  each  other  in  the  two  poles  of  the  Earth,  and  to  cles- 
cut  the  equator  M  at  every  15th  degree,  they  will 

be  divided  by  the  poles  into  24  semi-circles,  which 
divide  the  equator  into  24  equal  parts ;  and  as  the 
Earth  turns  on  its  axis,  the  planes  of  these  semicir- 
cles come  successively  one  after  another  every  hour 
to  the  Sun.     As  in  an  hour  of  time  there  is  a  revo-  An  hour 
lution  of  fifteen  degrees  of  the  equator,  in  a  minute 
of  time  there  will  be  a  revolution  of  15  minutes 
the  equator,  and  in  a  second  of  time  a  revolution  of  grees  of 
15  seconds.  There  are  two  tables  annexed  to  this1" 
chapter,  for  reducing  mean  solar  time  into  degrees 
and  minutes  of  the  terrestrial  equator ;  and  also  for 
converting  degrees  and  parts  of  the  equator  into 
mean  solar  time. 

209.  Because  the  Sun  enlightens  only  one  half  of 
the  Earth  at  once,  as  it  turns  round  its  axis,  he  rises 
to  some  places  at  the  same  moment  of  absolute  time 
that  he  sets  at  to  others ;  and  when  it  is  mid-day  to 
some  places,  it  is  mid-night  to  others.    The  XII  on 
the  middle  of  the  Earth's  enlightened  side,  next  the 
Sun,  stands  for  mid-day;  and  the  opposite  XII,  on 
the  middle  of  the  dark  side  for  midnight.     If  we 
suppose  this  circle  of  hours  to  be  fixed  in  the  plane 
of  the  equinoctial,  and  the  Earth  to  turn  round  with- 
in it,  any  particular  meridian  will  come  to  the  differ- 
ent hours  so  as  to  shew  the  true  time  of  the  day  or 
night  at  all  places  on  that  meridian.       Therefore, 

210.  To  every  place  15  degrees  eastward  from 
any  given  meridian,  it  is  noon  an  hour  sooner  than 
on  that  meridian;  because   their   meridian 


154  The  Method  of  finding  the  Longitude. 

to  the  Sun  an  hour  sooner;  and  to  all  places  15  de- 
grees westward,  it  is  noon  an  hour  later,  §  208,  be- 
cause their  meridian  comes  an  hour  later  to  the  Sun ; 
and  so  on  ;  every  15  degrees  of  motion  causing  an 
And  con-  hour's  difference  of  time.  Therefore  they  who  have 
sequently  noon  an  hour  later  than  we,    have  their  meridian, 
grees  of    tnat  is  their  longitude,  15  degrees  westward  from  us ; 
longitude,  and  they  who  have  noon  an  hour  sooner  than  we, 
have  their  meridian  15  degrees  eastward  from  ours ; 
and  so  for  every  hour's  difference  of  time,    15  de- 
Lunar  e-  grees  difference  of  longitude.     Consequently,  if  the 
usefuHn  Beginning  or  ending  of' a  lunar  eclipse  be  observed, 
finding  the  suppose  at  London,  to  be  exactly  at  midnight,  and 
longitude.  jn  some  other  place  at  11  at  night,  that  place  is  15 
degrees  westward  from  the  meridian  of  London  ;  if 
the  same  eclipse  be  observed  at  one  in  the  morning 
at  another  place,  that  place  is   15  degrees  eastward 
from  the  said  meridian. 

Eclipses        211.  But  as  it  is  not  easy  to  determine  the  exact 
terStel  rnoment  either  of  the  beginning  or  ending  of  a  lunar 
lites  mucii  eclipse,  because  the  Earth's  shadow  through  which 
61"  f°r  ^e  ^oon  Passes  *s  famt  an^  ill-defined  about  the 
J "  edges,  we  have  recourse  to  the  eclipses  of  Jupiter's 
satellites,  which  disappear  much  more  quickly  as 
they  enter  into  Jupiter's  shadow,  and  emerge  more 
suddenly  out  of  it.  The  first  or  nearest  satellite  to  Ju- 
piter is  the  most  advantageous  for  this  purpose,  be- 
cause its  motion  is  quicker  than  the  motion  of  any  of 
the  rest,  and  therefore  its  immersions  and  emersions 
are  more  frequent  and  more  sudden  than  those  of 
the  others  are. 

212  The  English  astronomers  have  calculated  ta- 
bles for  shewing  the  times  of  the  eclipses  of  Jupi- 
ter's satellites  to  great  precision,  for  the  meridian  of 
Greenwich.  Now,  let  an  observer,  who  has  these 
tables,  with  a  good  telescope  and  a  well-regulated 
clock,  at  any  other  place  of  the  Earth,  observe  the 


The  Method  of  finding  the  Longitude.  155 


beginning  or  ending  of  an  eclipse  of  one  of  Jupiter's  *£*  tor> 
satellites,  and  note  the  precise  moment  of  time  that  solve  this 
he  saw  the  satellite  either  immerge  into,  or  emerge  important 
out  of  the  shadow,  and  compare  that  time  with  thepr 
time  shewn  by  the  tables  for  Greenwich;  then,  15 
degrees  difference  of  longitude  being  allowed  for 
every  hour's  difference  of  time,  will  give  the  longi- 
tude of  that  place  from  Greenwich,  as  above,  §  210: 
and  if  there  be  any  odd  minutes  of  time,  for  every 
minute  a  quarter  of  a  degree,  east  or  west,  must  be 
allowed,  as  the  time  of  observation  is  later  or  earlier 
than  the  time  shewn  by  the  tables.     Such  eclipses 
are  very  convenient  for  this  purpose  on  land,   be- 
cause they  happen  almost  every  day  ;  but  are  of  no 
use  at  sea,  because  the  rolling  of  the  ship  hinders  all 
nice  telescopical  observations. 

213.  To  explain  this  by  a  figure,  let  /  be  Jupiter,  Fi£-  H. 
K,  L,  M,  N,  his  four  satellites  in  their  respective  lUustra- 
orbits,  1,  2,  3,  4;  and  let  the  Earth  be  at/  sup.^y« 
pose  in  November,  although  that  month  is  no  other- 

wise material  than  to  find  the  Earth  readily  in  this 
scheme,  where  it  is  shewn  in  eight  different  parts  of 
its  orbit.  Let  Q  be  a  place  on  the  meridian  of 
Greenwich,  and  R  a  place  on  some  other  meridian 
eastward  from  Greenwich.  Let  a  person  at  R  ob-  • 
serve  the  instantaneous  vanishing  of  the  first  satellite 
If  into  Jupiter's  shadow,  suppose  at  three  in  the 
morning  ;  but  by  the  tables  he  finds  the  immersion 
of  that  satellite  to  be  at  midnight  at  Greenwich;  he 
can  then  immediately  determine,  that,  as  there  are 
three  hours  difference  of  time  between  Q  and  R,  and 
that  R  is  three  hours  forwarder  in  reckoning  than  Q, 
it  must  be  in  45  degrees  of  east  longitude  from  the 
meridian  of  •  Q.  Were  this  method  as  practicable  at 
sea  as  on  land,  any  sailor  might  almost  as  easily,  and 
.with  almost  equal  certainty,  find  the  longitude  as  the 
latitude. 

214.  While  the  Earth  is  going  from  C  to  F  in  Fig.  IL 
its  orbit,  only  the  immersion  of  Jupiter's  satellites 


155  The  Method  of  finding  the  Longitude. 

domSSee  mto  n*s  shadow  are  generally  seen;  and  their  emer- 
the  beg-in-  sions  out  of  it  while  the  Earth  goes  from  G  to  B. — 
Tnd^oTtbe  Indeed>  both  tnese  appearances  may  be  seen  of  the 
same  e-  second,  third  and  fourth  satellite  when  eclipsed, 

anPoGf °Tfu  Wmle  ^ie  ^arth  *s  between  D  and  E,  or  between 
Piter's  6  and  A;  but  never  of  the  first  satellite,  on  account 
moons,  of  the  smallness  of  its  orbit  and  the  bulk  of  Jupiter, 
except  only  when  Jupiter  is  directly  opposite  to  the 
Sun,  that  is,  when  the  Eartfi  is  at  g:  and  even  then, 
strictly  speaking,  we  cannot  see  either  the  immer- 
sions or  emersions  of  any  of  his  satellites,  because 
his  body  being  directly  between  us  and  his  conical 
shadow  his  satellites  are  hid  by  his  body  a  few  mo- 
ments before  they  touch  his  shadow ;  and  are  quite 
emerged  from  thence  before  we  can  see  them,  as  it 
were,  just  dropping  from  behind  him.  And  when 
the  Earth  is  at  c,  the  Sun,  being  between  it  and  Ju- 
piter, hides  both  him  and  his  moons  from  us. 

In  this  diagram,  the  orbits  of  Jupiter's  moons 
are  drawn  in  true  proportion  to  his  diameter ;  but  in 
Jupiter's  proportion  to  the  Earth's  orbit,  they  are  drawn  81 
conjunc-   times  too  large. 

tii*8iBBb*  215*  In  whatever  month  of  the  year  Jupiter  is  in 
or  opposi-  conjunction  with  the  Sun,  or  in  opposition  to  him, 

him8  are     m  t^1C  nCXt  ^Caf  ^  W^  ^e  ^  montn  ^ater  at  ^east'    For 

every  year  while  the  earth  goes  once  round  the  Sun,  Jupiter  de- 

in  differ-   scribes  a  twelfth  part  of  his  orbit.    And,  therefore, 

of  SSL- when  the  Earth  has  finished  its  annual  period  from 

vens.        being  in  a  line  with  the  Sun  and  Jupiter,  it  must  go 

as  much  forwarder  as  Jupiter  has  moved  in  that  time, 

to  overtake  him  again :  just  like  the  minute-hand  of 

a  waxh,  which  must,  from  any  conjunction  with 

the   hour-hand,   go  once  round  the  dial-plate  and 

somewhat  above  a  twelfth  part  more,  to  overtake  the 

hour-hand  again. 

216.  It  is  found  by  observation,  that  when  the 
Earth  is  between  the  Sun  and  Jupiter,  as  at  g,  his 


The  Motion  of  Light  demonstrated.  157 

satellites  are  eclipsed  about  8  minutes  sooner  than  f^teiv. 
they  should  be  according  to  the  tables;  and  when 
the  Earth  is  at  B  or  C,  these  eclipses  happen  about 
8  minutes  later  than  the  tables  predict  them.*  Hence 
it  is  undeniably  certain,  that  the  motion  of  light  is 
not  instantaneous,  since  it  takes  about  16-  \  minutes 
of  time  to  go  through  a  space  equal  to  the  diameter 
of  the  Earth's  orbit  which  is  190  millions  of  miles 
in  length ;  and  consequently  the  particles  of  light  fly 
about  193  thousand  939  miles  every  second  of  time, 
which  is  above  a  million  of  times  swifter  than  the  mo- 
tion of  a  cannon  ball.  And  as  light  is  16^  minutes  The  sur- 
iii  travelling  across  the  Earth's  orbit,  it  must  be 
minutes  coming  from  the  Sun  to  us ;  therefore, 
the  Sun  were  annihilated,  we  should  see  him  for 
minutes  after ;  and  if  he  were  again  created,  he  would 
be  8^  minutes  old  before  we  could  see  him. 

217.  To  explain  the  progressive  motion  of  light,  Fig-  v- 
let  A  and  B  be  the  Earth,  in  two  different  parts  of 'niustwt- 
its  orbit,  whose  distance  from  each  other  is  95  mil-  ***  a  fi~ 
lions  of  miles,  equal  to  the  Earth's  distance  from 
the  Sun  S.  It  is  plain  that  if  the  motion  of  light 
were  instantaneous,  the  satellite  1  would  appear  to 
enter  into  Jupiter's  shadow  FF  &  the  same  moment 
of  time  to  a  spectator  in  A  as  to  another  in  B.  But 
by  many  years  observations  it  has  been  found,  that 
the  immersion  of  the  satellite  into  the  shadow  is  seen 
8£  minutes  sooner  when  the  Earth  is  at  B,  than 
when  it  is  at  A.  And  so,  as  Mr.  ROE  ME  a  first 
discovered,  the  motion  of  Light  is  thereby  proved 
to  be  progressive,  and  not  instantaneous,  as  was 
formerly  believed.  It  is  easy  to  compute  in  what 
time  the  Earth  moves  from  A  to  B ;  for  the  chord 
of  60  degrees  of  any  circle  is  .equal  to  the  semi- di- 
ameter of  that  circle;  and  as  the  Earth  goes  through 

*  In  the  tables  which  have  been  published  in  the  nautical  alma- 
nacs, &c.  a  proper  allowance  for  the  progress  ef  light  is  made. 


158  The  Motion  of  Light  demonstrated. 

all  the  360  degrees  of  its  orbit  in  a  year,  it  goes 
through  60  of  those  degrees  in  about  61  days, — 
Therefore,  if  on  any  given  day,  suppose  the  first  of 
June,  the  Earth  be  at  A,  on  the  first  of  August  it 
will  be  at  B :  the  chord,  or  straight  line  AB,  being 
equal  to  DS,  the  radius  of  the  Earth's  orbit,  the 
same  with  AS,  its  distance  from  the  Sun. 

218.  As  the  Earth  moves  from  D  to  C,  through 
the  side  AB  of  its  orbit,  it  is  constantly  meeting  the 
light  of  Jupiter's  satellites  sooner,  which  occasions 
an  apparent  acceleration  of  their  eclipses :  and  as  it 
moves  through  the  other  half  H  of  its  orbit  from  C 
to  Z),  it  is  receding  from  their  light,  which  occa- 
sions an  apparent  retardation  of  their  eclipses ;  be- 
cause their  light  is  then  longer  before  it  overtakes 
the  Earth. 

219.  That  these  accelerations  of  the  immersions 
of  Jupiter's  satellites  into  his  shadow,  as  the  Earth 
approaches  toward  Jupiter,  and  the  retardations  of 
their  emersions  out  of  his  shadow,  as  the  Earth  is 
going  from  him,  are  not  occasioned  by  any  inequal- 
ity arising  from  the  motions  of  the  satellites  in  ec- 
centric orbits,  is  plain,  because  it  affects  them  all 
alike,  in  whatever  parts  of  their  orbits  they  are  eclips- 
ed.    Besides,  they  go  often  round  their  orbits  every 
year,  and  their  motions  are  no  way  commensurate  to 
the  Earth's.     Therefore,  a  phenomenon,  not  to  be 
accounted  for  from  the  real  motions  of  the  satellites, 
but  so  easily  deducible  from  the  Earth's  motion,  and 
so  answerable  thereto,  must  be  allowed  to  result 
from  it.   This  affords  one  very  good  proof  of  the 
Earth's  annual  motion. 


7  0  convert  Motion  into  Time,  and  the  reverse. 


159 


'00.  Tables  for  converting  mean  solar  TIME  into  Degrees  and 
Parts  of  the  terrestrial  EQJJATOR  ;  and  also  for  converting  De- 
grees.and  Parts  of  the  EOJJATOR  into  mean  solar  TIME. 


TABLE!.    For  converting 
Time    into  Degrees  and 

TABLE  11.   For  converting   ' 
Degrees   and  Parts  of  the 

3arts  of  the  Equator. 

Equator  into  Time. 

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160 


Of  Solar  and  Sidereal  Time. 

These  are  the  tables  mentioned  in  the  208th  Ar- 
ticle, and  are  so  easy  that  they  scarce  require  any 
farther  explanation  than  to  inform  the  reader,  that  if, 
in  Table  I.  he  reckon  the  columns  marked  with  as- 
terisks  to  be  minutes  of  time,  the  other  columns  give 
the  equatorial  parts  or  motion  in  degrees  and  mi- 
nutes; if  he  reckon  the  asterisk- columns  to  be  se- 
conds, the  others  give  the  motion  in  minutes  and  se- 
conds of  the  equator;  if  thirds,  in  seconds  and 
thirds :  And  if  in  Table  II.  he  reckon  the  asterisk- 
columns  to  be  degrees  of  motion,  the  others  give 
the  time  answering  thereto  in  hours  and  minutes ;  if 
minutes  of  motion,  the  time  is  minutes  and  seconds; 
if  seconds  of  motion,  the  corresponding  time  is 
given  in  seconds  and  thirds.  An  example  in  each 
case  will  make  the  whole  very  plain. 


EXAMPLE  I. 

In  10  hours  15  mi- 
nutes 24  seconds  20 
thirds,  Qu.  How  much 
of  the  equator  revolves 
through  the  meridian  ? 

Deg.  M.  S. 

Hours  10       150    0     0 
Min.     15  3  45     0 

Sec.      24  6     0 

Thirds  20  5 


EXAMPLE  II. 

In  what  time  will  153 
degrees  5 1  minutes  5  se- 
conds of  the  equator 
revolve  through  the  me- 
ridian ? 

H.  M.S.T. 
150  10    0     0     0 
3        12     0     0 
Min.     51  3  24     0 

Sec.         5  20 


Deg.{ 


Armver         153  51     5     Answer     10  15  24  20 
CHAP.  XII. 

Of  Solar  and  Sidereal  Time. 

sidereal    Q91    r  I  ^HE  stars  appear  to  go  round  the  Earth 
daysshor.^1-  in  33  hours  55  minutes  4  seconds,  and 

t-or-  tl»an  ..  •- 


ter  than 


solar  days,  the  Sun  in  24  hours :  so  that  the  stars  gain  three 
and  why.  minutes  56  seconds  upon  the  Sun  every  day,  which 


Of  Solar  and  Sidereal  Time.  161 


amounts  to  one  diurnal  revolution  in  a  year  ; 
therefore,  in  365  days,  as  measured  by  the  returns 
of  the  Sun  to  the  meridian,  there  are  366  days,  as 
measured  by  the  stars  returning  to  it  :  the  former 
are  called  solar  days,  and  the  latter  sidereal  days. 

The  diameter  of  the  Earth's  orbit  is  but  a  phy- 
sical point  in  proportion  to  the  distance  of  the  stars  ; 
for  which  reason,  and  the  Earth's  uniform  motion 
on  its  axis,  any  given  meridian  will  revolve  from  any 
star  to  the  same  star  again  in  every  absolute  turn  of 
the  Earth  on  its  axis,  without  the  least  perceptible 
difference  of  time  shewn  by  a  clock  which  goes  ex- 
actly true. 

If  the  Earth  had  only  a  diurnal  motion,  without 
an  annual,  any  given  meridian  would  revolve  from 
the  Sun  to  the  Sun  again  in  the  same  quantity  of  time 
as  from  any  star  to  the  same  star  again  ;  because  the 
Sun  would  never  change  his  place  with  respect  to 
the  stars.  But,  as  the  Earth  advances  almost  a  de- 
gree eastward  in  its  orbit  in  the  time  that  it  turns  east- 
ward round  its  axis,  whatever  star  passes  over  the 
meridian  on  any  day  with  the  Sun,  will  pass  over  the 
same  meridian  on  the  next  day  when  the  Sun  is  al- 
most a  degree  short  of  it  ;  that  is,  3  minutes  56  se- 
conds sooner.  If  the  year  contained  only  360  days, 
as  the  ecliptic  doeb  360  degrees,  the  Sun's  apparent 
place,  so  far  as  his  motion  is  equable,  would  change 
a  degree  every  day  ;  and  then  the  sidereal  days  would 
be  just  4  minutes  shorter  than  the  solar. 

Let  ABCDEFGHIKLM  be  the  Earth's  orbit,  F;g.  n. 
in  which  it  goes  round  the  Sun  every  year,  accord- 
ing to  the  order  of  the  letters,  that  is,  from  west  to 
east;  and  turns  round  its  axis  the  same  way  from 
the  Sun  to  the  Sun  again  in  every  24  hour's.  Let  S 
be  the  Sun,  and  R  a  fixed  star  at  such  an  immense 
distance,  that  the  diameter  of  the  Earth's  orbit 
bears  no  sensible  proportion  to  that  distance.  Let 
N  m  be  any  particular  meridian  of  the  Earth,  and 
N  a  given  point  or  place  upon  that  meridian. 


162  Of  Solar  and  Sidenal  Time. 

When  the  Earth  is  at  A  the  Sun  S  hides  the  sta 
which  would  be  always  hid  if  the  Earth  never  remov- 
ed from  A;  and  consequently,  as  the  Earth  turns 
round  its  axis,  the  point  Ar would  always  come  round 
to  the  Sun  and  star  at  the  same  time.  But  when  the 
Earth  has  advanced,  suppose  a  twelfth  part  of  its  or- 
bit from  A  to  B,  its  motion  round  its  axis  will  bring 
the  point  JVa  twelfth  part  of  a  natural  day,  or  two 
hours,  sooner  to  the  star  than  to  the  Sun,  for  the  an- 
gle N  B  n  is  equal  to  the  angle  A  SB:  and  therefore 
any  star  which  comes  to  the  meridian  at  noon  with 
the  Sun  when  the  Earth  is  at  A,  .will  come  to  the 
meridian  at  10  in  the  forenoon  when  the  Earth  is  at 
B.  When  the  Earth  comes  to  C,  the  point  N  will 
have  the  star  on  its  meridian  at  8  in  the  morning,  or 
four  hours  sooner  than  it  comes  round  to  the  Sun  ; 
for  it  must  revolve  from  JVton  before  it  has  the  Sun 
in  its  meridian.     When  the  Earth  comes  to  Z),  the 
point  A*  will  have  the  star  on  its  meridian  at  6  in  the 
morning,  but  that  point  must  revolve  six  hours  more 
from  A*  to  ;z,  before  it  has  mid-day  by  the  Sun :  for 
now  the  angle  ASD  is  a  right  angle,  and  so  is  ND 
n  ;  that  is,  the  Earth  has  advanced  90  degrees  in  its 
orbit,  and  must  turn  90  degrees  on  its  axis  to  cany 
the  point  A*  from  the  star  to  the  Sun :  for  the  star  al- 
ways comes  to  the  meridian  when  A"  m  is  parallel  to 
R  S  A;  because  D  Sis  but  a  point  in  respect  to 
R  S.    When  the  Earth  is  at  E,  the  star  comes  to 
the  meridian  at  4  in  the  morning ;  at  F,  at  2  in  the 
morning;    and  at   G,  the  Earth  having  gone  half 
round  its  orbit,  A* points  to  the  star  R  at  midnight, 
it  being  then  directly  opposite  to  the  Sun.     And 
therefore,  by  the  Earth's  diurnal  motion,  the  star 
comes  to  the  meridian  12  hours  before  the  Sun. 
When  the  Earth  is  at  H,  the  star  comes  to  the  me- 
ridian at  10  in  the  evening ;  at  /  it  comes  to  the  me- 
ridian at  8,  that  is,  16  hours  before  the  Sun;  at  K 
18  hours  before  him;  atZ20  hours;  atJ/22;  and 
at  A  equally  with  the  Sun  again. 


Of  Solar  and  Sidereal  Time. 


163 


TABLE,  shewing  ho>v  much  of  the  Celestial  Equator 
passes  over  the  Meridian  in  any  Part  of  a  mean  SOLAR 
DAY;  and  how  much  the  FIXED  STARS  gum  upon  the 
mean  SOLAR  TIME  every  Day,  ibr  a  Month, 


165     27       6111  2    45     2' 
180    29    34 12    3       0 


164  Of  Solar  and  Sidereal  Time. 

Plate  in.      222.  Thus  it  is  plain,  that  an  absolute  turn  of 
Anabso-  tne  Earth  %on  its  axis  (which  is  always  completed 
lute  turn    when  any  particular  meridian  comes  to  be  parallel  to 
Earth  on    *ts  situati°n  at  any  time  of  the  day  before)  never 
its  axis      brings  the  same  meridian  round  from  the  Sun  to  the 
"fsbes!"    ^un  aSa*n»  kut  that  the  Earth  requires  as  much 
solar  day.  more  than  one  turn  on  its  axis  to  finish  a  natural  day, 
as  it  has  gone  forward  in  that  time ;  which,  at  a  mean 
state,  is  a  365th  part  of  a  circle.     Hence,  in  365 
days,  the  Earth  turns  366  times  round  its  axis  ;  and 
therefore,  as  a  turn  of  the  Earth  on  its  axis  com- 
pletes a  sidereal  day,  there  must  be  one  sidereal  day 
more  in  a  year  than  the  number  of  solar  days,  be  the 
number  what  it  will,  on  the  Earth,  or  any  other 
planet,  one  turn  being  lost  with  respect  to  the  num. 
her  of  solar  days  in  a  year,  by  the  planet's  going 
round  the  Sun ;  just  as  it  would  be  lost  to  a  travel- 
ler, who,  in  going  round  the  Earth,  would  lose  one 
day  by  following  the  apparent  diurnal  motion  of  the 
Sun ;  and  consequently  would  reckon  one  day  less 
at  his  return  (let  him  take  what  time  he  would  to  go 
round  the  Earth)  than  those  who  remained  all  the 
while  at  the  place  from  which  he  set  out. 

So,  if  there  were  two  Earths  revolving  equally  on 
Fig.  II.  their  axes,  and  if  one  remained  at  A  until  the  other 
had  gone  round  the  Sun  from  A  to  A  again,  that 
Earth  which  kept  its  place  at  A  would  have  its  solar 
and  sidereal  days  always  of  the  same  length ;  and  so 
would  have  one  solar  day  more  than  the  other  at  its 
return.  Hence,  if  the  Earth  turned  but  once  round 
its  axis  in  a  year,  and  if  that  turn  were  made  the  same 
way  as  the  Earth  goes  round  the  Sun,  there  would 
be  continual  day  on  one  side  of  the  Earth,  and  con- 
tinual night  on  the  other. 

223.  The  first  part  of  the  preceding  table  shews 
how  much  of  the  celestial  equator  passes  over  the 
meridian  in  any  given  part  of  a  mean  solar  day, 
and  is  to  be  understood  the  same  way  as  the  table 
in  the  220th  article.  The  latter  part,  intituled, 


Of  the  Equation  of  Time.  165 

Accelerations  of  the  fixed  Stars,  affords  us  an  easy  To  know 
method  of  knowing  whether  or  not  our  clocks  and  by  the 
watches  go  true  :  For  if,  through  a  small  hole  in  a  j^?  ™he~ 
window-shutter,  or  in  a  thin  plate  of  metal  fixed  to  clock  goes 
a  window,  we  observe  at  what  time  any  star  disap-  *™e  or 
pears  behind  a  chimney,  or  corner  of  a  house,  at  a 
little  distance  ;  and  if  the  same  star  disappear  the 
next  night  3  minutes  56  seconds  sooner  by  the  clock 
or  watch  ;  and  on  the  second  night,  7  minutes  52  se- 
conds sooner  ;  the  third  night  11  minutes  48  seconds 
sooner  ;  and  so  on,  every  night  as  in  the  table,  which 
shews  this  difference  for  30  natural  days,  it  is  an  in- 
fallible proof  that  the  machine  goes  true;  otherwise 
it  does  not  go  true,  and  must  be  regulated  accord- 
ingly ;  and  as  the  disappearing  of  a  star  is  instanta- 
neous, we  may  depend  on  this  information  to  half  a 
second. 

CHAP.  XIII. 

Of  the  Equation  of  Time. 


^24  V  1'^HE  Earth's  motion  on  its  axis  being  per- 
_1_  fectly  uniform,  and  equal  at  all  times  of 
the  year,  the  sidereal  days  are  always  precisely  of  an 
equal  length  ;  and  so  would  the  solar  or  natural  days 
be,  if  the  Earth's  orbit  were  a  perfect  circle,  and  its 
axis  perpendicular  to  its  orbit.  But  the  Earth's  di-  The  Sun 

i        *.  v       -.  i  .  ,  and  clocks 

urnal  motion  on  an  inclined  axis,  and  its  annual  mo-  equaioniy 
tion  in  an  elliptic  orbit,  cause  the  Sun's  apparent  mo-  on 
lion  in  the  heavens  to  be  unequal  :  for  sometimes  he 
revolves  from  the  meridian  to  the  meridian  again  in 
somewhat  less  than  24  hours,  shewn  by  a  well-regu- 
lated clock;  and  at  other  times  in  somewhat  more; 
so  that  the  time  shewn  by  an  equal-  going  clock  and 
a  true  Sun-dial  is  never  the  same  but  on  the  14th  of 
April,  the  15th  of  June,  the  31st  of  August,  and 
the  23d  of  December.     The  clock,  if  it  go  equa- 

blv  and  true  all  the  vear  round,  will  be  before  the 

*  * 


166  Of  the  Equation  of  Time. 

Sun  from  the  23d  of  December  till  the  14th  of  April; 
from  that  time  till  the  16th  of  June  the  Sun  will  be 
before  the  clock ;  from  the  15th  of  June  till  the  31st 
of  August  the  clock  will  be  again  before  the  Sun ; 
and  from  thence  to  the  23d  of  December  the  Sun 
will  be  faster  than  the  clock. 

use  of  the  -25.  The  tables  of  the  equation  of  natural  days, 
equation-  at  the  end  of  the  following  chapter,  shew  the  time 
that  ought  to  be  pointed  out  by  a  well  regulated 
clock  or  watch,  every  day  of  the  year,  at  the  pre- 
cise moment  of  solar  noon;  that  is,  when  the  Sun's 
centre  is  on  the  meridian,  or  when  a  true  sun-dial 
shews  it  to  be  precisely  twelve.  Thus,  on  the  5th 
of  January  in  leap-year,  when  the  Sun  is  on  the  me- 
ridian, it  ought  to  be  5  minutes  52  seconds  past 
twelve  by  the  clock :  and  on  the  15th  of  May,  when 
the  Sun  is  on  the  meridian,  the  time  by  the  clock 
should  be  but  56  minutes  1  second  past  eleven :  in 
the  former  case,  the  clock  is  5  minutes  52  seconds 
before  the  Sun ;  and  in  the  latter  case,  the,  Sun  is  3 
minutes  59  seconds  faster  than  the  clock.  But  with- 
out a  meridian-line,  or  a  transit- instrument  fixed  in  the 
plane  of  the  meridian,  we  cannot  set  a  sun-dial  true. 

HOW  to  226.  The  easiest  and  most  expeditious  way  of 
meridian-  drawing  a  meridian-line  is  this :  Make  four  or  five  con- 
line,  centric  circles,  about  a  quarter  of  an  inch  from  one  an- 
other,  oh  a  fiat  board  about  a  foot  in  breadth ;  and  let 
the  outmost  circle  be  but  little  less  than  the  board  will 
contain.  Fix  a  pin  perpendicularly  in  the  centre,  and 
of  such  a  length  that  its  whole  shadow  may  fall  within 
the  inner  most  circle  for  at  least  four  hours  in  the  mid- 
dle of  the  day.  The  pin  ought  to  be  about  an 
eighth  part  of  an  inch  thick,  and  to  have  a  round 
blunt  point.  The  board  being  set  exactly  level  in  a 
place  where  the  Sun  shines,  suppose  from  eight  in 
the  morning  till  four  in  the  afternoon,  about  which 
hours  the  end  of  the  shadow  should  fall  without 


Of  the  Equation  oj  Time.  *  10* 

all  the  circles;  watch  the  times  in  the  forenoon, 
when  the  extremity  of  the  shortening  shadow  just 
touches  the  several  circles,  and  there  make  marks. 
Then,  in  the  afternoon  of  the  same  day,  watch 
the  lengthening  shadow,  and  where  its  end  touches 
the  several  circles  in  going  over  them,  make 
marks  also.  Lastly,  with  a  pair  of  compasses,  find 
exactly  the  middle  point  between  the  two  marks  on 
any  circle,  and  draw  a  straight  line  from  the  centre 
to  that  point :  this  line  will  be  covered  at  noon  by 
the  shadow  of  a  small  upright  wire,  which  should 
be  put  in  the  place  of  the  pin.  The  reason  for  draw- 
ing several  circles  is,  that  in  case  one  part  of  the 
day  should  prove  clear,  arid  the  other  part  somewhat 
cloudy,  if  you  miss  the  time  when  the  point  of  the 
shadow  should  touch  one  circle,  you  may  perhaps 
catch  it  in  touching  another.  The  best  time  for 
drawing  a  meridian  line  in  this  manner  is  about  the 
summer  solstice  ;  because  the  Sun  changes  his  de- 
clination slowest  and  his  altitude  fastest  on  the  long- 
est days. 

If  the  casement  of  a  window  on  which  the  Sun 
shines  at  noon  be  quite  upright,  you  may  draw  a 
line  along  the  edge  of  its  shadow  on  the  floor, 
when  the  shadow  of  the  pin  is  exactly  on  the 
meridian  line  of  the  board  :  and  as  the  motion  of  the 
shadow  of  the  casement  will  be  much  more  sensible 
on  the  floor  than  that  of  the  shadow  of  the  pin  on 
the  board,  vou  may  know  to  a  few  seconds  when  it 
touches  the  meridian  line  on  the  floor;  and  so  regu- 
late your  clock  for  the  day  of  observation  by  that 
line  and  the  equation-tables  above  mentioned,  \  225. 

227.   As  the  equation   of   time,    or  difference  Equation 
between  the  time  shewn  by  a  well  regulated  clock  ^nf^al 
and  that  by  a  true  sun-dial,  depends  upon  two  caus-  pfained. 
es,  namely,  the  obliquity  of  the  ecliptic,  and  the 
unequal  motion  of  the  Earth  in  it;  we  shall  first 

Y 


168  i          Of  the  Equation  of  Time. 

explain  the  effects  of  these  causes  separately,  and 
then  the  united  effects  resulting  from  their  combi- 


a 
nation. 


228.    The    Earth's   motion   on   its  axis  being 

perfectly  equable,  or  always  at  the  same  rate,  and 

the*  plane  of  the  equator  being  perpendicular  to  its 

axis,  it  is  evident  that  m  equal  times  equal  portions 

of  the  equator  pass  over  the  meridian  ;  and  so  would 

equal  portions  of  the  ecliptic,  if  it  were  parallel  to 

The  first  or  coincident  with  the  equator.    But,  as  the  ecliptic 

part  of  the  js  oblique  to  the  equator,  the  equable  motion  of  the 

equation     -,-,       ,     *        .  L     -,  .  *>    i  i» 

of  time.  Earth  carries  unequal  portions  of  the  ecliptic  over 
the  meridian  in  equal  times,  the  difference  being 
proportionate  to  the  obliquity ;  and  as  some  parts  of 
the  ecliptic  are  much  more  oblique  than  others, 
those  differences  are  unequal  among  themselves. 
Therefore  if  two  Suns  should  start  either  from 
the  beginning  of  Aries  or  of  Libra,  and  continue  to 
move  through  equal  arcs  in  equal  times,  one  in  the 
equator,  and  the  oth^r  in  the  ecliptic,  the  equatorial 
Sun  would  always  return  to  the  meridian  in  24  hours 
time,  as  measured  by  a  well-regulated  clock ;  but 
the  Sun  in  the  ecliptic  would  return  to  the  meridian 
sometimes  sooner,  and  sometimes  later  than  the 
equatorial  Sun  ;  and  only  *at  the  same  moments  with 
him  on  four  days  of  the  year ;  namely,  the  20th  of 
March,  when  the  Sun  enters  Aries;  the  21st  of 
June,  when  he  enters  Cancer ;  the  23d  of  Septem- 
ber, when  he  enters  Libra;  and  the  21st  of  Decem- 
ber, when  he  enters  Capricorn.  But,  as  there  is 
only  one  Sun,  and  his  apparent  motion  is  always  in 
the  ecliptic,  let  us  henceforth  call  him  the  real  Sure, 
and  the  other,  which  is  supposed  to  move  in  the 

*  If  the  Earth  were  cut  along  the  equator,  quite  through  the  cen- 
tre, the  flat  surface  of  this  section  would  be  the  plane  of  the  equa- 
tor ;  as  the  paper  contained  within  any  circle  may  be  justly  termed 
the  plane  of  that  circle. 


Of  the  Equation  of  Time.  169 

equator,  the  fictitious :  to  which  last,  the  motion  of  Plate  vi. 
a  well- regulated  clock  always  answers. 

Let  Z  T  z  =2=  be  the  Earth,  ZFRz  its  axis.,  Fig.  in, 
abcde,&c.  the  equator,  ABCDE,&.c.\h(t  northern  half 
of  the  ecliptic  from  *v»  to  =0=  on  the  side  of  the  globe 
next  the  eye,  and  MNOP,  &c.  the  southern  half  on 
the  opposite  side  from  =&  to  r.  Let  the  points  at 
y/,  .#,  C,  Z),  E,  F,  &c.  quite  round  from  v  to  T 
again,  bound  equal  portions  of  the  ecliptic,  gone 
through  in  equal  times  by  the  real  Sun ;  and  those 
at  #,  &,  r,  of,  ?,/;  &c.  equal  portions  of  the  equator 
described  in  equal  times  by  the  fictitious  Sun ;  and 
let  Z  «¥>  z  be  the  meridian. 

As  the  real  Sun  moves  obliquely  in  the  ecliptic, 
and  the  fictitious  Sun  directly  in  the  equator,  with 
respect  to  the  meridian,  a  degree,  or  any  number  of 
degrees,  between  «p  and  F  on  the  ecliptic,  must  be 
nearer  the  meridian  Z  «y»  z,  than  a  degree,  or  any 
corresponding  number  of  degrees,  on  the  equator 
from  IT  to/;  and  the  more  so,  as  they  are  the  more 
oblique .:  and  therefore  the  true  Sun  comes  sooner  to 
the.  meridian  every  day  while  he  is  in  the  quadrant 
T  F)  than  the  fictitious  sun  does  in  the  quadrant  *¥* 
f;  for  which  reason,  the  solar  noon  precedes  noon 
by  the  clock,  until  the  real  Sun  comes  to  F,  and  the 
fictitious  to/;  which  two  points,  being  equidistant 
from  the  meridian,  both  suns  will  come  to  it  pre- 
cisely at  noon  by  the  clock. 

While  the  real  Sun  describes  the  second  qua- 
drant of  the  ecliptic  FGHIKL  from  <&  to  =a»,  he 
comes  later  to  the  meridian  every  day  than  the  fic- 
titious sun  moving  through  the  second  quadrant  of 
the  equator  from/"  to  =2=;  for  the  points  at  G,  H,  /, 
K,  and  L,  being  farther  from  the  meridian  than  their 
corresponding  points  at  g,  h,  i,  k,  and  /,  they  must 
be  later  in  coming  to  it .  and  as  both  suns  come  at 
the  same  moment  to  the  point  ^,  they  come  to  the 
meridian  at  the  moment  of  noon  by  the  clock. 


170  Of  the  Equation  of  Time. 

In  departing  from  Libra,  through  the  third  quad- 
rant, the  real  Sun  going  through  MNOPQ  toward 
X?  at  7i,  and  the  fictitious  sun  through  mnopq  toward 
r;  the  former  comes  to  the  meridian  every  day  soon- 
er than  the  latter,  until  the  real  Sun  comes  to  V5 ,  and 
the  fictitious  to  r,  and  then  they  both  come  to  the 
meridian  at  the  same  time. 

Lastly,  as  the  real  Sun  moves  equably  through 
STUFIV,  from  v?  toward  r ;  and  the"  fictitious 
sun  through  sfuvw,  from  r  toward  T,  the  former 
comes  later  every  day  to  the  meridian  than  the  lat- 
ter, until  they  both  arrive  at  the  point  V,  and  then 
they  make  it  noon  at  the  same  time  with  the 
clock. 

229.  The  annexed  table  shews  how  much  the 

Sun  is  faster  or  slower  than  the  clock  ought  to  be, 

so  far  as  the  difference  depends  upon  the  obliquity 

of  the  ecliptic ;  of  which  the  signs  of  the  first  and 

A  table  of  third  quadrants  are  at  the  head  of  the  table,  and  their 

tion<oTa   degrees  at  the  left  hand ;  and  in  these  the  Sun  is 

time  de.    faster  than  the  clock  :  the  signs  of  the  second  and 

pending    fourth  quadrants  are  at  the  foot  of  the  table,  and  their 

Sun's6       degrees  at  the  right  hand ;  in  all  which  the  Sun  is 

place  in    slower  than  the  clock ;  so  that  entering  the  table 

theechp-  ^^  ^  gjven  sjgn  of  tne  Sun's  place  at  the  head 

of  the  table,  and  the  degree  of  his  place  in  that  sign 
at  the  left  hand;  or  with  the  given  sign  at  the 
foot  of  the  table,  and  degree  at  the  right  hand ; 
in  the  angle  of  meeting  is  the  number  of  minutes 
and  seconds  that  the  Sun  is  faster  or  slower  than 
the  clock :  or,  in  other  words,  the  quantity  of  time 
in  which  the  real  Sun,  when  in  that  part  of  the 
ecliptic,  comes  sooner  or  later  to  the  meridian 
than  the  fictitious  sun  in  the  equator.  Thus, 
when  the  Sun's  place  is  8  Taurus  12  degrees,  he 
is  9  minutes  47  seconds  faster  than  the  clock; 


Of  the  Equation  of  Time. 

and  when  his  place  is  25  Cancer  18  degrees,  he  Is  6 
minutes  2  seconds  slower. 


171 


Sun  faster  than  the  Clock  in 

C 

T 

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1st    Ci- 

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3d    Q. 

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Deg. 

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,      < 

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7*46 

30 

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3     35 

*9 

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J    41 

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24 

7 

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J     24 

r    2' 

23 

8 

1    37 

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7       t 

22 

9 

J     5t 

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6     50 

21 

10 

J     15 

9     4(. 

6    35 

20 

11 

>     3-. 

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5     Ib 

19 

12 

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3 

18 

13 

4    '11 

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17 

14 

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16 

15 

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J     53 

5       t 

15 

16 

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14 

17 

2( 

3     54 

4     31 

13 

18 

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'J     5  , 

t     1) 

12 

19 

5; 

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J     5. 

11 

20 

0 

y     4 

>     32 

10 

21 

25 

>   4e 

3     1- 

9 

22 

4( 

'     4. 

>     5' 

8 

23 

5     54 

•» 

•      o  - 

-•     30 

7 

24 

r         c 

9     3? 

2       < 

6 

25 

7     22 

9     2f 

1     4^ 

5 

26 

7     36 

9     1' 

t      !Ct 

4 

27 

;•'     4fc 

9     1 

t 

3 

28 

s     c 

9       4 

.t     4 

2 

29 

y    12 

8     55 

fi     2' 

1 

30 

S    23 

8     4t 

)       ( 

0 

2d     Q. 

"nJT 

a 

25 

4th   (£ 

X 

VJ 

Deg: 

Sun  silver  tk'in  thp  Clock  in      j 

This  table  is  formed  by  taking  the  difference  be- 
tween the  Sun's  longitude  and  its  right  ascension, 
and  turning  it  into  time. 


172  Of  the  Equation  of  Time. 

Plate  in.  230.  This  part  of  the  equation  of  time  may  per- 
Fig  in.  haps  be  somewhat  difficult  to  understand  by  a  figure, 
because  both  halves  of  the  ecliptic  seem  'to  be  on 
the  same  side  of  the  globe :  but  it  may  be  made  very 
easy  to  any  person  who  has  a  real  globe  before  him, 
by  putting  small  patches  on  every  tenth  or  fifteenth 
degree  both  of  the  equator  and  ecliptic,  beginning 
at  Aries  T  ;  and  then  turning  the  ball  slowly  round 
westward,  he  will  see  all  the  patches  from  Aries  to 
Cancer  come  to  the  brazen  meridian  sooner  than  the 
corresponding  patches  on  the  equator  ;  all  those  from 
Cancer  to  Libra  will  come  later  to  the  meridian  than 
their  corresponding  patches  on  the  equator ;  those 
from  Libra  to  Capricorn  sooner,  and  those  from 
Capricorn  to  Aries  later ;  and  the  patches  at  the  be- 
ginnings of  Aries,  Cancer,  Libra,  and  Capricorn, 
being  either  on  or  even  with  those  on  the  equator, 
shew  that  the  two  suns  either  meet  there,  or  are  even 
with  one  another,  and  so  come  to  the  meridian  at 
the  same  moment. 

A  ma-  231.  Let  us  suppose  that  there  are  two  little  balls 
shewin*  movmg  equably  round  a  celestial  globe  by  clock- 
theli'df-  work,  one  always  keeping  in  the  ecliptic,  and  gilt 
real, the  w^h  ffold,  to  represent  the  real  Sun;  and  the  other 

equal,  and ,          . °      .      A*  ,    .,  , 

the  solar  keeping  in  the  equator,  and  silvered,  to  represent  the 
time.  fictitious  sun  :  and  that  while  these  balls  move  once 
round  the  globe  according  to  the  order  of  signs,  the 
clock  turns  the  globe  366  times  round  its  axis  west- 
ward. The  stars  will  make  366  diurnal  revolutions 
from  the  brazen  meridian  to  it  again,  and  the  two 
balls  representing  the  real  and  fictitious  suns  always 
going  farther  eastward  from  any  given  star,  will  come 
later  than  it  to  the  meridian  every  following  day  : 
and  each  ball  will  make  365  revolutions  to  the 
meridian  ;  coming  equally  to  it  at  the  beginnings 
of  Aries,  Cancer,  Libra,  and  Capricorn  ;  but  in 
every  other  point  of  the  ecliptic,  the  gilt  ball  will 

come  either  sooner  or  later  to  the  meridian  than  the 
I 


Of  the  Equation  of  Time,  173 

silvered  ball,  like  the  patches  above-mentioned.  This  Plate  VL 
would  be  a  pretty  way  enough  of  shewing  the  rea- 
son why  any  given  .star,  which,  on  a  certain  day  of 
the  year,  conies  to  the  meridian  with  the  Sun,  pas- 
ses over  it  so  much  sooner  every  following  day,  as 
on  that  day  twelvemonth  to  come  to  the  meridian 
with  the  Sun  again ;  and  also  to  shew  the  reason 
why  the  real  Sun  comes  to  the  meridian  sometimes 
sooner,  and  sometimes  later,  than  the  time  when  it 
is  noon  by  the  clock ;  and  on  four  days  of  the  year, 
at  the  same  time ;  while  the  fictitious  sun  always 
conies  to  the  meridian  when  it  is  twelve  at  noon  by 
the  clock.  This  would  be  no  difficult  task  for  an 
artist  to  perform ;  for  the  gold  ball  might  be  carried 
round  the  ecliptic  by  a  wire  from  its  north  pole,  and 
the  silver  ball  round  the  equator  by  a  wire  from  its 
south  pole,  by  means  of  a  few  wheels  to  each; 
which  might  be  easily  added  to  my  improvement  of 
the  celestial  globe,  described  in  N°  483  of  the  Phi- 
losophical Transactions  ;  and  of  which  I  shall  give  a 
description  in  the  latter  part  of  this  book,  from  the 
third  figure  of  the  third  plate. 

232.  It  is  plain  that  if  the  ecliptic  were  more  ob-  Fig.  iTl 
liquely  posited  to  the  equator,  as  the  dotted  circle  T  x 
d^,  the  equal  divisions  from  Ttox  would  come  still 
sooner  to  the  meridian  Z  0  T  than  those  marked 
A,  B,  C,  Z),  and  E,  do :  for  two  divisions  contain- 
ing 30  degrees,  from  v  to  the  second  dot,  a  little 
short  of  the  figure  1 ,  come  sooner  to  the  meridian 
than  one  division  containing  only  15  degrees  from  T 
to  A  does,  as  the  ecliptic  now  stands  ;  and  those  of 
the  second  quadrant  from  x  to  ^  would  be  so  much 
later.  The  third  quadrant  would  be  as  the  first,  and 
the  fourth  as  the  second.  And  it  is  likewise  plain, 
that  where  the  ecliptic  is  most  oblique,  namely, 
about  Aries  and  Libra,  the  difference  would  be 
greatest;  and  least  about  Cancer  and  Capricorn, 
where  the  obliquity  is  least. 


174  Of  the  Equation  of  Time, 

Plate  vi.       234.  Having  explained  one  cause  of  the  differ. 
The  se-     ence  of  time  shewn  by  a  well-regulated  clock  and  a 
S?lthe>art  ** ue  sun'dial,  and  considered  the  bun,  not  the  Earth, 
equation    as  moving  in  the  ecliptic,   we  now  proceed  to  ex- 
oftime.     plain  the  other  cause  of  this  difference,  namely,  the 
inequality  of  the  Sun's   apparent   motion,    \  205, 
which  is  slowest  in  summer,  when  the  Sun  is  far- 
thest from  the  Earth,  and  swiftest  in  winter  when  he 
is  nearest  to  it.     But  the  Earth's  motion  on  its  axis 
is  equable  all  the  year  round,  and  is  performed  from 
west  to  east ;  which  is  the  way  that  the  Sun  appears 
to  change  his  place  in  the  ecliptic. 

235.  If  the  Sun's  motion  were  equable  in  the 
ecliptic,  the  whole  difference  between  the  equal  time 
as  shewn  by  the  clock,  and   the  unequal  time  as 
shewn  by  the  Sun,  would  arise  from  the  obliquity  of 
the  ecliptic.    But  the  Sun's  motion  sometimes  ex- 
ceeds a  degree  in  24  hours,   though  generally  it  is 
less ;  and  when  his  motion  is  slowest,  any  particular 
meridian  will  revolve  sooner  to  him  than  when  his 
motion  is  quickest ;  for  it  will  overtake  him  in  less 
time  when  he  advances  a  less  space  than  when  he 
moves  through  a  larger. 

236.  Now,  if  there  were  two  suns  moving  in  the 
plane  of  the  ecliptic,  so  as  to  go  round  it  in  a  year ; 
the  one  describing  an  equal  arc  every  24  hours,  and 
the  other  describing  sometimes  a  less  arc  in  24 
hours,  and  at  other  times  a  larger ;  gaining  at  one 
time  of  the  year  what  it  lost  at  the  opposite;   it  is 
evident  that  either  of  these  suns  would  come  sooner 
or  later  to  the  meridian  than  the  other,  as  it  happen- 
ed to  be  behind  or  before  the  other :  and  when  they 
were  both  in  conjunction,  they  would  come  to  the 
meridian  at  the  same  moment. 

237.  As  the  real  Sun  moves  unequably  in  the 
ecliptic,   let  us  suppose  a  fictitious  sun   to  move 

Fig.  iv.    equably  in  a  circle   coincident  with  the  plane  of 
the  ecliptic.     Let  A  BCD  be  the  ecliptic  or  orbit 


Of  the  Equation  of  Time.  175 

in  which  the  real  Sun  moves,  and  the  dotted  circle 
a,  b>  c,  d,  the  imaginary  orbit  of  the  fictitious  sun ; 
each  going  round  in  a  year  according  to  the  order 
of  letters,  or  from  west  to  east*  Let  HIKL  be  the 
Earth  turning  round  its  axis  the  same  way  every  24 
hours  ;  and  suppose  both  suns  to  start  from  A  and 
a,  in  a  right  line  with  the  plane  of  the  meridian 
EH,  at  the  same  moment :  the  real  Sun  at  A,  being 
then  at  his  greatest  distance  from  the  Earth,  at  which 
time  his  motion  is  slowest ;  and  the  fictitious  sun  at 
a,  whose  motion  is  always  equable,  because  his  dis- 
tance from  the  Earth  is  supposed  to  be  always  the 
same.  In  the  time  that  the  meridian  revolves  from 
If  to  H  again,  according  to  the  order  of  the  letters 
HIKL,  the  real  Sun  has  moved  from  A  to  F;  and 
the  fictitious,  with  a  quicker  motion,  from  a  to  f, 
through  a  larger  arc  ;  therefore,  the  meridian  E  H 
will  revolve  sooner  from  Hto  h  under  the  real  Sun 
at  F,  than  from  //to  Sunder  the  fictitious  sun  aty> 
and  consequently  it  will  then  be  noon  by  the  sun* 
dial  sooner  than  by  the  clock* 

As  the  real  Sun  moves  from  A  toward  C,  the 
swiftness  of  his  motion  increases  all  the  way  to  C, 
where  it  is  at  the  quickest.  But  notwithstanding 
this,  the  fictitious  sun  gains  so  much  upon  the  real, 
soon  after  his  departing  from  A,  that  the  increasing 
velocity  of  the  real  Sun  does  not  bring  him  up  with 
the  equably-moving  fictitious  sun  till  the  former 
comes  to  C,  and  the  latter  to  r,  when  each  has  gone 
half  round  its  respective  orbit ;  and  then,  being  in 
conjunction,  the  meridian  E  H  revolving  to  E  K 
comes  to  both  Suns  at  the  same  time,  and  therefore 
it  is  noon  by  them  both  at  the  same  moment. 

But  the  increased  velocity  of  the  real  Sun,  now 
being  at  the  quickest,  carries  him  before  the  ficti- 
tious one ;  and,  therefore,  the  same  meridian  will 
come  to  the  fictitious  sun  sooner  than  to  the  real : 
for  while  the  fictitious  sun  moves  from  c  to  g,  the 
real  Sun  moves  through  a  greater  arc  from  C  to  O: 
consequently  the  point  .AT  has  its  noon  by  the  clock 

Z 


1 76  Of  the  Equation  of  Time. 


PLATE 
VI. 


when  it  comes  to  £,  but  not  its  noon  by  the  Sun 
till  it  comes  to  /.  And  although  the  velocity  of  the 
real  Sun  diminishes  all  the  way  from  C  to  A,  and 
the  fictitious  sun  by  an  equable  motion  is  still  com- 
ing nearer  to  the  real  Sun,  yet  they  are  not  in  con- 
junction  till  the  one  comes  to  A,  and  the  other  to  a; 
and  then  it  is  noon  by  them  both  at  the  same  mo- 
ment. 

Thus  it  appears,  that  the  solar  noon  is  always 

later  than  noon  by  the  clock  while  the  Sun  goes 

from  C  to  A;  sooner,  while  he  goes  from  A  to  C, 

and  at  these  two  points,  the  Sun  and  clock  being 

equal,  it  is  noon  by  them  both  at  the  same  moment. 

Apogee,        238.  The  point  A  is  called  the  Sun's  apogee^  be- 

and  apt*    cause  when  he  is  there,  he  is  at  his  greatest  distance 

sides,       from  the  Earth ;  the  point  C,  his  perigee,  because 

what-       when  in  it  he  is  at  his  least  distance  from  the  Earth  : 

Fi£- 1V-    and  a  right  line,  as  AEC,  drawn  through  the  Earth's 

centre,  from  one  of  these  points  to  the  other,  is 

called  the  line  of  the  apsides. 

239.  The  distance  that  the  Sun  has  gone  in  any 
time  from  his  apogee  (not  the  distance  he  has  to  go 

Meanano-to  it,  though  ever  so  little)  is  called  his  mean  ano- 
what'.  maly,  and  is  reckoned  in  signs  and  degrees,  allow- 
ing  30  degrees  to  a  sign.  Thus,  when  the  Sun  has 
gone  174  degrees  from  his  apogee  at  A,  he  is  said 
to  be  5  signs  24  degrees  from  it,  which  is  his  mean 
anomaly;  and  when  he  has  gone  355  degrees  from 
his  apogee,  he  is  said  to  be  11  signs  25  degrees 
from  it,  although  he  be  but  5  degrees  short  of  A, 
in  coming  round  to  it  again. 

240.  From  what  was  said  above,  it  appears,  that 
when  the  Sun's  anomaly  is  less  than  6  signs,  that 
is,  when  he  is  any  where  between  A  and  C,  in  the 
half  ABC  of  his  orbit,  the  solar  noon  precedes  the 
clock- noon ;  but  when  his  anomaly  is  more  than  6 
signs,  that  is,  when  he  is  any  where  between  C  and 
A,  in  the  half  CDA  of  his  orbit,  the  clock-noon  pre- 
cedes the  solar.     When  his  anomaly  is  0  signs, 
0  degrees,  that  is,  when  he  is  in  his  apogee  at  A; 


Of  the  Equation  of  Time.  1 77 

or  6  signs,  0  degrees,  which  is  when  he  is  in  his  pe- 
rigee at  C;  he  comes  to  the  meridian  at  the  moment 
that  the  fictitious  sun  does,  and  then  it  is  noon  by 
them  both  at  the  same  instant. 

241.  The  following  table  shews  the  variation,  or 
equation  of  time  depending  on  the  Sun's  anomaly, 
and  arising  from  his  unequal  motion  in  the  ecliptic ; 
as  the  former  table,  §  229,  shews  the  variation  de- 
pending on  the  Sun's  place,  and  resulting  from  the 
obliquity  of  the  ecliptic :  this  is  to  be  understood  the 
same  way  as  the  other,  namely,  that  when  the  signs 
are  at  the  head  of  the  table,  the  degrees  are  at  the 
left  hand  ;  but  when  the  signs  are  at  the  foot  of  the 
table,  the  respective  degrees  are  at  the  right  hand ; 
and  in  both  cases  the  equation  is  in  the  angle  of  meet- 
ing. When  both  the  above-mentioned  equations  are 
either  faster  or  slower,  their  sum  is  the  absolute 
equation  of  time  ;  but  when  the  one  is  faster,  and 
the  other  slower,  it  is  their  difference.  Thus  sup- 
pose the  equation  depending  on  the  Sun's  place  be 
6  minutes  41  seconds  too  slow,  and  the  equation 
depending  on  the  Sun's  anomaly,  4  minutes  20  se- 
conds too  slow,  their  sum  is  eleven  minutes  one  se- 
cond too  slow.  But  if  the  one  had  been  6  minutes 
41  seconds  too  fast,  and  the  other  4  minutes  20  se- 
conds too  slow,  their  difference  would  have  been  2 
minutes  2 1  seconds  too  fast,  because  the  greater 
quantity  is  too  fast. 


178 


Of  the  Equation  of  Time. 


S      Sun  faster  than  the  Clock  if  his  anomaly  be     S 


A  Table 
of  the 
equation 
of  time, 
depending1 
on  the 
Sun's  ano^ 
maty. 


s 

a  Siimb1 

1 

2 

3 

4 

5 

s 

• 

S 

D 

M.  S 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

M.  S. 

!* 

s 

'-'""-"- 

RW 

~-  ~  ~  ^  - 

™  •—*•*•• 

-~~     *"" 

s 

0 

0    0 

3  47 

6  36 

7  43 

6   45 

3   56 

30  S 

t 

0    8 

3   54 

6  40 

/  43 

6  41 

3  49 

29  5 

2 

0   16 

4    1 

6  44 

7  43 

6  37 

3   41 

28  S 

3 

0   24 

4   8 

6  48 

7  43 

6  32 

3  34 

27$ 

4 

0   32 

4   14 

6   52 

7  42 

6  28 

3  27 

26S 

S  5 

0   40 

4  21 

6   56 

7  42 

6   24 

3   19 

25? 

S  6 

0   47 

4  27 

6  59 

7  41 

6   19 

3   12 

24  S 

S  ? 

0   55 

4  34 

7   2 

7  40 

6   14 

3   4 

23? 

S  8 

1    3 

4  40 

7   6 

7  39 

6   9 

2   57 

22  S 

S  9 

1    11 

4  47 

7   9 

7  38 

6   4 

2  49 

21  ? 

SlO 

19 

4  53 

7   12 

7  37 

5   59 

2  41 

20  S 

|u 

27 

4   59 

7   14 

r  36 

5   54 

2  34 

19? 

Sl2 

34 

5   5 

7   17 

7  35 

5   49 

2  26 

18  w 

5  13 

42 

5   11 

7  20 

7  33 

5   43 

2   18 

17$ 

S  14 

50 

5   17 

7  2.2 

7  31 

5   38 

2   10 

16> 

57 

5  22 

24 

7  29 

5   32 

2   2 

\$ 

*i€ 

2    5 

5  28 

27 

7  27 

5  26 

1   54 

S  17 

2   13 

5  34 

29 

7  25 

5   20 

1   46 

13  S 

S18 

2   20 

5  39 

31 

7  23 

5   14 

1   38 

12  s 

>  19 

2   28 

5   44 

32 

7  20 

5    8 

1   30 

US 

S20 

2   35 

5   50 

34 

7   18 

5   2 

1   22 

10  S 

?2l 

2   43 

5   55 

35 

7   15 

4   56 

1   14 

9  c 

*22 

2   50 

6   0 

37 

7   12 

4   50 

I    6 

8  V 

c  23 

2   57 

6   5 

38 

7   9 

4  43 

0  58 

7S 

S24 

3    5 

6   10 

7  39 

7   6 

4  37 

0  49 

6  ' 

S  25 

3   12 

6   14 

7  40 

7   3 

4  30 

0  41 

5  S 

S  26 

3   19 

6   19 

7  41 

7   0 

4  23 

0   33 

4  ' 

<27 

3   26 

6  24 

7  41 

6  56 

4   17 

0  25 

3S 

?28 

3   33 

6  28 

7   42 

6  53 

4   1C 

0   17 

2V 

S29 

3   40 

6  32 

7  42 

6  49 

4   3 

0   8 

1  S 

^  30 

3   47 

6  36 

7  43 

6  45 

3   56 

0   0 

OS 

S 

1  iSign 

10 

9 

8 

7 

6 

D-s 

This  table  is  formed  by  turning  the  equation  of 
the  Sun's  centre  (see  p.  344)  into  time. 

242.  The  obliquity  of  the  ecliptic  to  the  equator, 
which  is  the  first  mentioned  cause  of  the  equation 
of  time,  would  make  the  Sun  and  clock  agree  on 


Of  the  Equation  of  Time.  179 

four  days  of  the  year ;  namely,  when  the  Sun  enters 
Aries,  Cancer,  Libra,  and  Capricorn  :  but  the  other 
cause,  now  explained,  would  make  the  Sun  and 
clock  equal  only  twice  in  a  year ;  that  is,  when  the 
Sun  is  in  his  apogee,and  in  his  perigee.  Consequently, 
when  these  two  points  fall  in  the  beginnings  of  Can- 
cer  and  Capricorn,  or  of  Aries  and  Libra,  they  con- 
cur in  making  the  Sun  and  clock  equal  in  these 
points.  But  the  apogee  at  present  is  in  the  9th  de- 
gree of  Cancer,  and  the  perigee  in  the  9th  degree 
of  Capricorn ;  and  therefore  the  Sun  and  clock 
cannot  be  equal  about  the  beginnings  of  these  signs, 
nor  at  any  time  of  the  year,  except  when  the  swift- 
ness or  slowness  of  the  equation  resulting  from  one 
cause  just  balances  the  slowness  or  swiftness  arising 
from  the  other. 

243.  The  second  table  in  the  following  chapter 
shews  the  Sun's  place  in  the  ecliptic  at  the  noon  of 
every  day  by  the  clock,  for  the  second  year  after 
leap-year  ;  and  also  the  Sun's  anomaly  to  the  near- 
est degree,  neglecting  the  odd  minutes  of  that  de- 
gree. Its  use  is  only  to  assist  in  the  method  of 
making  a  general  equation- table  from  the  two  fore- 
mentioned  tables  of  equation  depending  on  the  Sun's 
place  and  anomaly,  §  229,  241 ;  concerning  which 
method  we  shall  give  a  few  examples  presently.  The 
next  tables  which  follow  them  are  made  from  those 
two ;  and  shew  the  absolute  equation  of  time  result- 
ing from  the  combination  of  both  its  causes ;  in  which 
the  minutes  as  well  as  degrees,  both  of  the  Sun's 
place  and  anomaly,  are  considered.  The  use  of 
these  tables  is  already  explained,  §  225 :  and  they 
serve  for  every  day  in  leap-year,  and  the  first,  se- 
cond, and  third  years  after :  For  on  most  of  the 
same  days  of  all  these  years  the  equation  differs, 
because  of  the  odd  six  hours  more  than  the  365  days 
of  which  the  year  consists. 

EXAMPLE  I.  On  the  14th  of  April,  the  Sun  is  m|^S£" 
the  25th  degree  of  r  Aries  and  his  anomaly  is  9  ing  equa- 
signs  15  degrees;  the  equation  resulting  from  the  tion*tables* 


1 80  Of  the  Equation  of  Time. 

former  is  7  minutes  22  seconds  of  time  too  fast, 
§  229;  and  from  the  latter,  7  minutes  24  seconds 
too  slow,  \  241 ;  the  difference  is  2  seconds  that  the 
Sun  is  too  slow  at  the  noon  of  that  day,  taking  it  in 
gross  for  the  degrees  of  the  Sun's  place  and  ano- 
maly, without  making  proportionable  allowance  for 
the  odd  minutes.  Hence  at  noon,  the  swiftness  of 
the  one  equation  balancing  so  nearly  the  slowness 
of  the  other,  makes  the  Sun  and  clock  equal  on 
some  part  of  that  day. 

EXAMPLE  II.  On  the  16th  of  June,  the  Sun  is 
in  the  25th  degree  of  n  Gemini,  and  his  anomaly 
is  11  signs  16  degrees;  the  equation  arising  from 
the  former  is  1  minute  48  seconds  too  fast ;  and 
from  the  latter  1  minute  50  seconds  too  slow ;  which 
balancing  one  another  at  noon  to  2  seconds,  the  Sun 
and  clock  are  again  equal  on  that  day. 

EXAMPLE  III.  On  the  Slstofdugtist,  the  Sun's 
place  is  8  degrees  11  minutes  of  i#  Virgo  (which 
we  call  the  8th  degree,  as  it  is  so  near),  and  his  ano- 
maly is  1  sign  29  degrees ;  the  equation  arising  from 
the  former  is  6  minutes  40  seconds  too  slow ;  and 
from  the  latter,  6  minutes  32  seconds  too  fast ;  the 
difference  being  only  8  seconds  too  slow  at  noon, 
and  decreasing  toward  an  equality,  will  make  the 
Sun  and  clock  equal  in  the  evening  of  that  day. 

EXAMPLE  IV.  On  the  23d  of  December,  the 
Sun's  .place  is  1  degree  58  minutes  (call  it  2  degrees 
of  V3  Capricorn),  and  his  anomaly  is  5  signs  23  de- 
grees ;  the  equation  for  the  former  is  43  seconds  too 
slow,  and  for  the  latter  58  seconds  too  fast ;  the  dif- 
ference is  15  seconds  too  fast  at  noon ;  which  de- 
creasing will  come  to  an  equality,  and  so  make  the 
Sun  and  clock  equal  in  the  evening  of  that  day. 

And  thus  we  find,  that  on  some  part  of  each  of 
the  above-mentioned  four  davs,  the  Sun  and  clock 


Of  the  Precession  of  the  Equinoxes*  18  r 

are  equal ;  but  if  we  work  examples  for  all  other  days 
of  the  year,  we  shall  find  them  different.    And, 

244.  On  those  days  which  are  equidistant  from 
any  equinox  or  solstice,  we  do  not  find  that  the 
equation  is  as  much  too  fast  or  too  slow  on  the  one 
side,  as  it  is  too  slow  or  too  fast  on  the  other.  The 
reason  is,  that  the  line  of  the  apsides,  §  238,  does  Remark, 
not,  at  present,  fall  either  into  the  equinoctial  or  the 
solstitial  points,  §  242. 

245.  The  four  following  equation- tables,  for  leap-  The  rea- 
year,  and  the  first,  second,  and  third  years  after,  son  why 
would  serve  for  ever,  if  the  Sun's  place  and  anomaly  tablet  a"ii 
were  alwavs  the  same  on  every  given  day  of  the  year,  but  tem- 
as  on  the  same  day  four  years  before  or  after.  Butporarv 
since  that  is  not  the  case,  no  general  equation-tablets 

can  be  so  constructed  as  to  be  perpetual. 


CHAP.  XIV. 

Of  the  Precession  of  the  Equinoxes. 

TT  has  been  already  observed,  §  116,  that  by 
'  J[  the  Earth's  motion  on  its  axis,  there  is  more 
matter  accumulated  all  around  the  equatorial  parts, 
than  any  where  else  on  the  Earth. 

The  Sun  and  Moon,  by  attracting  this  redundancy 
of  matter,  bring  the  equator  sooner  under  them  in 
every  return  towards  it,  than  if  there  was  no  such 
accumulation.  Therefore,  if  the  Sun  sets  out  from 
any  star,  or  other  fixed  point  in  the  heavens,  the 
moment  when  he  is  departing  from  the  equinoctial, 
or  from  either  tropic ;  he  will  come  to  the  same 
equinox  or  tropic  again  20  min.  17|  sec.  of  time, 
or  50  seconds  of  a  degree,  before  he  completes  his 
course,  so  as  to  arrive  at  the  same  fixed  star  or  poini: 
from  whence  he  set  out.  For  the  equinoctial  point-, 
recede  50  seconds  of  a  degree  westward  every  year, 
contrary  to  the  Sun's  annual  progressive  motion. 


182  Of  the  Precession  of  the  Equinoxes. 

PLATE  When  the  Sun  arrives  at  the  same*  equinoctial 
or  solstitial  point,  he  finishes  what  we  call  the  tropi- 
cal year  ;  which,  by  observation,  is  found  to  con- 
tain  365  days  5  hours  48  minutes  57  seconds :  and 
when  he  arrives  at  the  same  fixed  star  again,  as  seen 
from  the  Earth,  he  completes  the  sidereal  year, 
which  contains  365  days  6  hours  9  minutes  14|  se- 
conds. The  sidereal  year  is  therefore  20  minutes 
17-J  seconds  longer  than  the  solar  or  tropical  year, 
and  9  minutes  14j  seconds  longer  than  the  Julian 
or  civil  year,  which  we  state  at  365  days  6  hours: 
so  that  the  civil  year  is  almost  a  mean  betwixt  the 
sidereal  and  the  tropical. 

247.  As  the  Sun  describes  the  whole  ecliptic,  or 
360  degrees,  in  a  tropical  year,  he  moves  59'  8"  of 
a  degree  every  day  at  a  mean  rate :  and  consequently 
50'  of  a  degree  in  20  minutes  17^  seconds  of  time: 
therefore  he  will  arrive  at  the  same  equinox  or  sol- 
stice when  he  is  50"  of  a  degree  short  of  the  same 
star  or  fixed  point  in  the  heavens  from  which  he  set 
out  the  year  before.  So  that,  with  respect  to  the 
fixed  stars,  the  Sun  and  equinoctial  points  fall  back 
(as  it  were)  30  degrees  in  2160  years,  which  will 
make  the  stars  appear  to  have  gone  30  deg.  forward, 
with  respect  to  the  signs  of  the  ecliptic  in  that  time : 
for  the  same  signs  always  keep  in  the  same  points 
of  the  ecliptic,  without  regard  to  the  constellations. 
Fig.  iv  To  explain  this  by  a  figure,  let  the  Sun  be  in  con- 
junction with  a  fixed  star  at  S,  suppose  in  the  30th 
degree  of  8,  on  the  21st  day  of  May  1756.  Then 
making  2160  revolutions  through  the  ecliptic  VWX, 


*  The  two  opposite  points  in  which  the  ecliptic  crosses 
the  equinoctial,  are  called  the  equinoctial  points :  and  the  two 
points  where  the  ecliptic  touches  the  tropics  (which  are 
likewise  opposite,  and  90  degrees  from  the  former)  are 
called  ike  solstitial  ficints. 


Of  the  Precession  of  the  Equinoxes.  183 


0'; 


S -  TABLE  shewing  the  Precession  of  the  Equinoctial  Points  in  the\ 
Heavens^  both  in  Motion  and  Time ;  and  the  Anticipation  of  the  ^ 
Equinoxes  on  the  Earth. 


1 

Julian 
years. 

Recession  of  the  Equinoctial  Points 
in  the  Heavens. 

Anticipation  of  the  s 
Equinoxes     on  $ 
the  Earth.           s 

s; 

Motion. 

Time. 

s.       0        '      " 

Days   H.  M.      S. 

D.     H.    M.     S.  !» 

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0        0     55      15  S 

6 

7 
8 
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10 
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0        7     22        OS 
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70 
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2        7      15        0^ 
3        1      40        0  > 
3     20        5        OS 
4      14     3.0       0  J* 
5        8     55        Os 

800 
900 
1000 
2000 
3000 

4000 
5000 
6000 
.       7000 
8000 

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7      16      10      ,0«! 

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1000 
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198     21      36       OS 

184  Of  the  Precession  of  the  Equinoxes. 

at  the  end  of  so  many  sidereal  years,  he  will  be  found 
again  at  AS:  but  at  the  end  of  so  many  Julian  years, 
he  will  be  found  at  My  short  of  S,  and  at  the  end  of 
so  many  tropical  years,  he  will  be  found  short  of  M, 
in  the  30th  degree  of  Taurus  at  J1,  which  has  reced- 
ed back  from  S  to  T  in  that  time,  by  the  precession 
of  the  equinoctial  points  <f  Aries  and  ^=  Libra. 

The  arc  ST  will  be  equal  to  the  amount  of  the 
precession  of  the  equinox  in  2160  years  at  the  rate 
of  50''  of  a  degree,  or  20  min.  17-|  sec.  of  time  an- 
nually :  this,  in  so  many  years,  makes  30  days  lOf 
hours  :  which  is  the  difference  between  2160  side- 
real and  tropical  years.  And  the  arc  MT  will  be  equal 
to  the  space  moved  through  by  the  Sun  in  2160 
times  11  min.  3  sec.  or  16  days  13  hours  48  mi- 
nutes, which  is  the  difference  between  2160  Julian 
and  tropical  years. 

248.  From  the  shifting  of  the  equinoctial  points, 
and  with  them  all  the  signs  of  the  ecliptic,  it  follows 
that  those  stars  which  in  the  infancy  of  astronomy 
were  in  Aries  are  now  got  into  Taurus:  those  of 
Taurus  into  Gemini,  &tc.  Hence  likewise  it  is,  that 
the  stars  which  rose  or  set  at  any  particular  season 
of  the  year,  in  the  times  of  HESIOD,  EUDOXUS, 
VIRGIL,  PLINY,  &c.  by  no  means  answer  at  this 
time  to  their  descriptions.  The  preceding  table 
shews  the  quantity  of  this  shifting  both  in  the  hea- 
vens and  on  the  Earth,  for  any  number  of  years  to 
25,920;  which  completes  the  grand  celestial  peri- 
od  :  within  which  any  number  and  its  quantity  is 
easily  found,  as  in  the  following  example,  for  5763 
years;  which  at  the  autumnal  equinox,  A.  D.  1756, 
is  thought  to  be  the  age  of  the  world.  So  that  with 
regard  to  the  fixed  stars,  the  equinoctial  points  in 
the  heavens  have  receded  2s  20°  2'  30"  since  the 
creation  ;  which  is  as  much  as  the  Sun  moves  in 
in  81d  5f>  Ora  52s.  And  since  that  time,  or  in  5763 
years,  the  equinoxes  with  us  have  fallen  back  44d 
5h  21m  9s  ;  hence,  reckoning  from  the  time  of  the 
Julian  equinox,  A.  D.  1756,  viz.  Sept.  llth,  it 


Of  the  Precession  of  the  Equinoxes. 

appears  that  the  autumnal  equinox  at  the  creation 
was  on  the  25th  of  October. 


185 


j^vy-sX\/-w/\r\ 

S  Julian 
^  years. 

is 

r*r*r^r*r<J*>r'*rjr*rJ**'**r*r'-J'^'>f  **''*''*'•*'<* 

Precesssion  of  the  Equinoctial 
Points  in  the  Heavens. 

^•+r*rs*r*r*r.  $fc 

Anticipation  £ 
of  the  Equi-   «, 
noxes  on  the  S 
Earth.             ? 

\ 

Motion. 

TLne. 

s     0      '2* 

D.  H.  M.  S. 

D.H.M.S.  £ 

t. 

J>  5000 
S  700 
^  60 

2     9     26     40 
0     9     43     20 
O     0     50       O 
O     0       2     3O 

70  10  58  20 
9  20  44  10 
020  17  30 
0  1  O52 

38    850  0\ 
5    8  55  0  Jj 
Oil     3  OS 
O   O  33   9  s 

£  5763 

2     20     2     30 

81     5    O52 

44     5  21  9  S 

249.  The  anticipation  of  the  equinoxes,  and  con-  J 
sequently  of  the  seasons,  is  by  no  means  owing  to  thequL- 
the  precession  of  the  equinoctial  and  solstitial  points  noxes  an 
in  the  heavens  (which  can  only  affect  the  apparent se 
motions,  places  and  declinations  of  the  fixed  stars) 

but  to  the  difference  between  the  civil  and  solar 
year,  which  is  11  minutes  3  seconds  \  the  civil  year 
containing  365  days  6  hours,  and  the  solar  year 
365  days  5  hours  48  minutes  57  seconds.  The  next 
following  table,  page  189,  shews  the  length,  and 
consequently  the  difference  of  any  number  of  side- 
real, civil  and  solar  years,  from  1  to  10,000. 

250.  The  above  11  minutes  3  seconds,  by  which  The  rea- 
the  civil  or  Julian  year,  exceeds  the  solar,  amounts  teSn^t 
to  11  days  in  1433  years:  and  so  much  our  seasons  style, 
have  fallen  back  with  respect  to  the  days  of  the 
months,  since  the  time  of  the  Nicene  council  in 

A,  D.  325  ;  and  therefore,  in  order  to  bring  back  all 
the  fasts  and  festivals  to  the  days  then  settled,  it  was 
requisite  to  suppres  1 1  nominal  days.  And  that 
the  same  seasons  might  be  kept  to  tfre  same  times 
of  the^  year  for  the  future,  to  leave  out  the  Bissex- 


186  Of  the  Precession  of  the  Equinoxes. 

PLATE  tile-day  in  February  at  the  end  of  every  century  of 
years  where  the  significant  figures  are  not  divisible 
by  4 ;  reckoning  them  only  common  years,  as  the 
17th,  18th,  and  19th  centuries,  viz.  the  years 
1700,  1800,  1900,  &c.  because  a  day  intercalated 
every  fourth  year  was  too  much,  and  retaining  the 
Bissextile-day  at  the  end  of  those  centuries  of  years 
which  are  divisible  by  4,  as  the  16th,  20th  and  24th 
centuries;  viz.  the  years  1600,  2000,  2400,  &c. 
Otherwise,  in  length  of  time,  the  seasons  would  be 
quite  reversed  with  regard  to  the  months  of  the 
year;  though  it  would  have  required  near  23,783 
years  to  have  brought  about  such  a  total  change.  If 
the  Earth  had  made  exactly  365J  diurnal  rotations 
on  its  axis,  while  it  revolved  from  any  equinoctial 
or  solstitial  point  to  the  same  again,  the  civil  and  so- 
lar years  would  always  have  kept  pace  together,  and 
the  style  would  never  have  required  any  alteration. 
the  pre-  251.  Having  already  mentioned  the  cause  of  the 
cesssion  of  precession  of  the  equinoctial  points  in  the  heavens, 
noctiai11*  &  ^6,  which  occasions  a  slow  deviation  of  the 
points.  Earth's  axis  from  its  parallelism,  and  thereby  a 
change  of  the  declination  of  the  stars  from  the  equa- 
tor, together  with  a  slow  apparent  motion  of  the 
stars  forward  with  respect  to  the  signs  of  the  eclip- 
tic, we  shall  now  explain  the  phenomena  by  a  dia- 
gram. 

Fig.  vi.  Let  NZS7L  be  the  Earth,  SONA  its  axis  pro- 
cluced  to  the  starry  heavens,  and  terminating  in  A, 
the  present  north  pole  of  the  heavens,  which  is  ver- 
tical to  JV,  the  north  pole  of  the  Earth.  Let  EOQ 
be  the  equator,  T  95  Zt  the  tropic  of  Cancer,  and 
VT  x?  the  tropic  of  Capricorn  :  70 Z  the  ecliptic, 
and  BO  its  axis,  both  which  are  immoveable  among 
the  stars.  But  as  *  the  equinoctial  points  recede  in 

*  The  equinoctial  circle  intercepts  the  ecliptic  in  two  opposite 
points ;  namely,  the  ferst  points  of  the  signs  Aries  and  Libra.  They 
are  called  the  equinoctial  points,  because  when  the  bun  is  in  either 


Of  the  Precession  of  the  Equinoxes.  187 

the  ecliptic,  the  Earth's  axis  SON  is  in  motion 
upon  the  Earth's  centre  O,  in  such  a  manner  as  to 
describe  the  double  cone  JVOn  and  Sos,  round  the 
axisof  the  ecliptic,  BO,  in  the  time  that  the  equinoctial 
points  move  quite  round  the  ecliptic,  which  is  25, 920 
years;  and  in  that  length  of  time  the  north  pole  of  the 
Earth's  axis  produced,  describes  the  circled?  CZ)^, 
in  the  starry  heavens,  round  the  pole  of  the  ecliptic, 
which  keeps  immoveable  in  the  centre  of  that  circle, 
the  Earth's  axis  being  23|  degrees  inclined  to  the 
axis  of  the  ecliptic,  the  circle  ABC  D  A,  described 
by  the  north  pole  of  the  Earth's  axis  produced  to 
A,  is  47  degrees  in  diameter,  or  double  the  inclina- 
tion of  the  Earth's  axis.  In  consequence  of  this  mo- 
tion, the  point  A,  which  at  present  is  the  north  pole 
of  the  heavens,  and  near  to  a  star  of  the  second  mag- 
nitude in  the  tail  of  the  constellation  called  the  Lit- 
tle Bear,  must  be  deserted  by  the  Earth's  axis; 
which  moving  backward  a  degree  every  72  years, 
will  be  directed  toward  the  star  or  point  B  in  6480 
years  from  this  time ;  and  in  twice  that  time,  or 
12960  years,  it  will  be  directed  toward  the  star  or 
point  C:  which  will  then  be  the  north  pole  of  the 
heavens,  although  it  is  at  present  8~  degrees  south 
of  the  zenith  of  London  L,  The  present  position 
of  the  equator  EOQ  will  then  be  changed  into  eOg, 
the  tropic  of  Cancer  T<s  Z  into  Vt  25  and  the  tro- 
pic of  Capricorn  FT  v?  into  /  >5  Z;  as  is  evident 
by  the  figure ;  and  the  Sun,  when  in  that  part  of  the 
heavens,  where  he  is  now  over  the  terrestrial  tropic 
of  Capricorn,  and  makes  the  shortest  days  and 
longest  nights  in  the  northern  hemisphere,  will  then 
be  over  the  terrestrial  tropic  of  Cancer,  and  make 
the  days  longest  and  nights  shortest.  And  it  will 
require  12,960 years  more,  or  25,920  from  the  pre- 

of  them,  he  is  directly  over  the  terrestrial  equator :  and  then  the  day* 
and  nights  are  equal. 


188  Of  the  Precession  of  the  Equinoxes. 

sent  time,  to  bring  the  north  pole  N  quite  round,  so 
as  to  be  directed  toward  that  point  of  the  heavens 
which  is  vertical  to  it  at  present.  And  then,  and  not 
till  then,  the  same  stars,  which  at  present  describe 
the  equator,  tropics,  polar  circles,  &c.  by  the  Earth's 
diurnal  motion,  will  describe  them  over  again. 


Of  Sidereal,  Julian,  and  Solar  Time.  185 

TABLE  shewing  the    Time  contained  in  any  Number  of  Sidereal,  Julian, 
and  Solar  Years,  from  1  to  10000. 


Sidereal  Years. 

Julian  Years,  j]    Solar  Years. 

___ 
S. 

fears.  |  D  ys  |  H.  |  M. 

S. 

Days. 

H.  ||  Days.  |  H.  M. 

1 

365 

6 

9 

141 

365 

6 

365 

5 

4b 

57 

C) 

£ 

730 

12 

18 

29 

730 

12 

73( 

11 

37 

54 

o 

1095 

18 

27 

43-£ 

1095 

18 

1095 

17 

26 

51 

4 

1461 

0 

36 

58 

1461 

0 

146C 

23 

15 

48 

c 

1826 

6 

4C 

121 

1826 

6 

1826 

5 

4 

45 

€ 

2191 

12 

55 

27 

2191 

12 

2191 

10 

53 

42 

7 

2556 

19 

5 

44 

2556 

18 

2556 

16 

42 

39 

8 

2,922 

1 

13 

56 

2922 

0 

2921 

22 

31 

36 

9 

3287 

7 

23 

101 

3287 

el 

3287 

4 

20 

33 

10 

3652 

13 

32 

25 

3652 

12 

3652 

10 

9 

30 

20 

7305 

3 

4 

50 

7305 

0 

7304 

20 

19 

0 

30 

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16 

37 

15 

10957 

12 

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28 

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14 

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25566 

2 

6 

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80 

29220 

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19 

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16 

0 

90 

32873 

1 

51 

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12 

32871 

19 

25 

30 

100 

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15 

24 

10 

36525 

36524 

5 

35 

200 

73051 

6 

48 

20 

73050 

73048 

n 

10 

300 

109576 

22 

12 

30 

109575 

109572 

16 

45 

400 

146102 

13 

36 

40 

146100 

146096 

22 

20 

500 

182628 

5 

0 

50 

182625 

182621 

o 

55 

600 

219153 

20 

25 

219150 

219145 

9 

30 

700 

255679 

11 

49 

10 

255675 

255669 

15 

5 

800 

292205 

3 

13 

20 

292200 

292193 

20 

40 

900 

228730 

18 

37 

30  ' 

328725 

328718 

2 

15 

1000 

365256 

10 

1 

40 

365250 

365242 

7 

50 

2000 

730512 

20 

3 

20 

730500 

730484 

15 

40 

3000 

1095769 

6 

5 

1095750 

1095720 

23 

30 

4000 

1461025 

16 

6 

40 

1461000 

1460969 

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90 

5000 

1826282 

2 

8 

20 

1826250 

1826211 

IS 

10 

6000 

2191538 

12 

10 

2191500 

2191453 

23 

o 

7000 

2556794 

22 

11 

40 

2556750 

2556696 

c 

50 

8000 

2952051 

8 

13 

20 

292200C 

2921938 

14 

40 

9000 
10000 

K*yy* 

3287037 
3652564 

fVVyw 

18 
4 
,r,r.r,, 

15 
16 

r^W 

40 

V*Wy\^ 

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3652500 

^vr,^,/-^^ 

<-^y*,r 

3287180 
365242S 

XV",r^V%^« 

22 
6 

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30 
20 
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190 


Tables  of  the  Surfs 


A  TABLE  shewing  the  Sun's  true  Place,  and  Distance  from  its  S 
Apogee,  for  the  second  Year  after  Leap-Year. 


5 

January-       |      February. 

March. 

April.           J 

s  o 

Sun's 

Sun's 

Sun's  1  Sun's 

Sun's 

Sun's 

Sun's 

Sun's   S 

5i 

Place. 

Anom. 

Place.  1  Anom. 

Place. 

Anom  . 

Place. 

Anom.  <J 

i»  f 

D.  M.  |  D.  M. 

D.  vi.     D    '  . 

1).  M.  |  D.  M.|D.  M 

D.  M.  \ 

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11X523 

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12—56 

7        4 

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13      57 

7        5 

12      10 

8       3 

12      56 

9        4  ^ 

S    3 

13      25 

6        4 

14      58 

7        6 

13     10 

8        4 

13      55 

9        5S 

S    4 

14     27 

6        5 

15      58 

7       7 

14      10 

8        5 

i4      54 

9     6  J; 

5 

15      28 

6        6 

16      59 

7       8 

15      10 

8        6 

15      53 

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?"" 

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16     29 

6        7 

18      00 

7        9 

16      10 

8        7 

16     52 

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j 

17     30 

6        8 

19      0! 

7      10 

17      10 

8        8 

17     51 

9       8  !j 

S     8 

18     31 

6        9 

20     01 

7      11' 

18      10 

8        9 

18     49 

9        9  S 

9 

19     32 

6      10 

21      02 

7      12 

19     09 

8      10 

19     48 

9      10  § 

10 

20     34 

6      11 

22     03 

7      13 

20     09 

8      11 

20     47 

9      11  S 

11 

21      35 

6,     12 

23     03 

7      14 

21      09 

8      12 

21      46 

9      12  S 

12 

22     36 

6      13 

24     04 

7      15 

22     09 

8      13 

22      44 

9      13  5 

13 

23     37 

6      14 

25      04 

7      16 

23     09 

8      14 

23      43 

9      14  S 

14 

24     38 

6      15 

26     05 

7     17 

24     08 

8      15 

24     42 

9      15  < 

" 

25      39 

6      16 

27     06 

7      18 

25      08 

8      16 

25      40 

9      16  Jj 

flS 

26     40 

6      17 

28      06 

7      19 

26     08 

8      17 

26      39 

9      17  S 

S17 

27     42 

6      18 

29      07 

7     20 

27     07 

8      18 

27     38 

9      18  Ij 

?I8 

28     43 

6      19 

X      07 

7     21 

28      07 

8      19 

28     36 

9      19  S 

S  19 

29     44 

6     20 

1      07 

7     22 

29      06 

8      20 

29      35 

9     20!; 

^  20 

y~     45 

6     21 

2     08 

7     23 

cy      06 

8     21 

«       33 

9     21  S 

ill 

1     46 

6      22 

3     08 

7     24 

1      05 

8      22 

1      32 

9      22  S 

S22 

2     47 

6     23 

4     08 

7     25 

2     05 

8      23 

2      30 

9     23  ? 

**  23 

3     48 

6     24 

5     09 

7     26 

3      04 

8     2* 

3      28 

9     24  S 

S  24 

4     49 

6     25 

6     09 

7     27 

4     03 

8      25 

4     27 

9     25  ^ 

5  25 

5      50 

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7     09 

7     28 

5      03 

8     26 

5     25 

9      26  S 

c 

2 

^ 

V     At  V 

6      51 

6     28 

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7      29 

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6     23 

9      27  ? 

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6     29 

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8        0 

7     01 

8     28 

7     21 

9      28  s 

^28 

8     53 

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8      00 

8      29 

8     20 

9      29  *s 

S29 

9     53 

7        1 

9     00 

9        0 

9      18 

10       0  > 

5  30 

10      54 

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9      59 

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10      16 

10        1  S 

S31 

11      55 

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10      58 

9        2 

S 
S 

*.                                                                                                       .    »    '•i^ 

W,                                                                                                                                                                                                 " 

Place  and  Anomaly. 


191 


A  TABLE  shewing  the  Sim's  true  Place,  and  Distance  from  its 
Apogee,  for  the  second  Year  after  Leap- Year. 


t 

May. 

June. 

July. 

August. 

s  e 

Sun's 

Sun's 

Sun's 

Sun's 

Sun's 

Sun's 

Sun's 

Sun's 

S   W! 

Place. 

Anom. 

Place. 

Anom. 

Place. 

Anom. 

Place. 

Anom. 

S  ' 

D.  M. 

S.  D. 

D.  M. 

S.  D. 

D.  M. 

S.   D. 

D.  M. 

S.   D. 

S  i 

U  014 

10   2 

11  D04 

11    2 

99542 

0    0 

D&1S 

0 

S  2 

12   12 

10   3 

12   01 

11   3 

10   39 

0    1 

10   16 

1 

S  S 

13   10 

10   4 

12   59 

11    A 

11   37 

0   2 

11   13 

2 

S  4 

14  08 

10    5 

13   56 

11    5 

12   34 

0   3 

!2   11 

3 

15   06 

10    6 

14   53 

11   e 

13   31 

0   4 

13  08 

4 

S  — 

16  04 

10   7 

15   51 

11    6 

14  28 

0    5 

14  06 

5 

7 

17   02 

10   8 

16   48 

11   7 

i  5   2  5 

0   6 

15   03 

6 

5  R 

18  00 

10   9 

17  46 

11    8 

16  23 

0   7 

1  6  0  i 

7 

s 

S  9 

18   58 

10   10 

18   43 

11    9 

17   20 

0   8 

16   58 

8 

•jo 

19   56 

10   11 

19   40 

11   10 

18   17 

0   9 

17   56 

1   9 

s~ 

20   54 

10   12 

20   38 

11   11 

19   14 

0   10 

18   54 

1   10 

%)s 

21   52 

10   12 

21   35 

11   12 

20   12 

0   11 

19   51 

I   10 

22   49 

10   13 

22   32 

11   13 

21   09 

0   12 

20   49 

1   11 

S  14 

23   47 

10   14 

23   30 

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22   06 

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:i  47 

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S  15 

24   45 

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S  lfi 

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11   18 

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SS19 

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28   16 

11   19 

26   53 

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29   34 

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a  31 

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55   10 

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28  47 

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1   19 

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29   44 

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29   29 

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^23 

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10  23 

2   05 

11   23 

SI   42 

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1   21 

3   24 

10   24 

3  02 

11   24 

1   39 

0   22 

I   25 

1   22 

$23 

t 

4  22 

10   25 

3   59 

11   25 

2   36 

0   23 

2   23 

i   23 

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10   26 

4   5611   26 

3   34 

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$27 

6   17 

10  27 

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J-28 

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<J  29 

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7   13 

1   28 

S 

S  31 

10  06 

:  1    1 

8  21 

0   29 

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Bb 


192 


Tables  of  the  Swfs  Place,  fcfc. 


"  >*  -^  <*  >^^  «^  ^•^^f^f^'^r^- jf^f^-^-^-^r^-^  *r  ,w  ^*r^  .  i^ys 

t\  TABLE  shewing  the  Sun's  true  Place,  and  Distance  from  its'S 
Apogee,  for  the  second  Year  after  Leap-Year. 


1     September. 

October. 

November. 

December.      £ 

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SUD'S  \ 

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Sun's 

Sun's 

Sun's    Jj 

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Anom. 

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D.    M. 

S.      D. 

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S.      D. 

D.    M. 

S.      D. 

D.    M. 

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V  S 


TABLES 


OF  THE. 


EQUATION  OF  TIME* 


FOR 


LEAP-YEARS  AND  COMMON  YEARS  ; 


Shewing  what  Time  it  ought  to  be  by  the  Clock 
when  the  Sun's  Centre  is  on  the  Meridian. 


194 


Equation-Tables. 


S  A  TABLE    shewing  what  Time  it  ought  to  be  by  the  Clock's 

S                     when  the  Sun's  Centre  is  on  the  Meridian.                      v, 

S                                 The  Bissextile  or  Leap-Year.                                 Jj 

S   £? 

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«i                                                                                .  . 

195 


JA 

s  — 


TABLE  shewing  what  Time  it  ought  to  be  by  the 
Clock  when  the  Sun's  Centre  is  on  the  Meridian. 
The  Bissextile,  or  Leap^-Ycar. 


II 

s  ^ 

1 

May. 

June. 

July. 

August 

'       S 

H. 

M. 

S.[H. 

M. 

S 

II. 

M. 

S. 

H.     M. 

XI 

56 

48JXI 

57 

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XII 

3 

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A  TABLE  shewing  what  Time  it  ought  to  be  by  the  S 
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Equation*  Tables. 


201 


S  A  TABLE  shewing  what  Time  it  ought  to  be  by  the 
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Equation-  Tables. 


TABLE  shewing  what  Time  it  ought  to  be  by  the 
Clock  when  the  Min's  Centre  is  on  the  Meridian. 
The  second  Year  after  Leap-Year. 


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Equation-Tables. 


203 


TABLE  shewing  what  Time  it  ought  to  be  by  the 
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>                     The  third  Year  alter  Leap-  Year. 

>   0 

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2      43 

1 

y 

XII       6     2 
6      5 
7      1 
7     4 
8 

Xll     14      32 
14      35 
14     37 
14     39 

14      40 

XII    11      31 
11      17 
10        2 
10      46 
10     31 

XII  2      25 
2        8 
1      51 
1      34 
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XI  59      58 

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14 
15 

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9      1 
9      3 
9      5 

Xli      14     40 
14      39 
14     37 
14      35 
14      31 

XII    10      14 

9      58 
9      41 

9      24 
9        7 

16 
S  l7 
S  18 

S  19 

|S 

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S23 

24 
25 

XII      10      2 
10     3 
10      5 
11       1 
11      3 

XII      14     27 

14     23 
14      17 
14      11 
14        5 

Xll     8      49 
8      32 
8      14 
7      55 
7     37 

XI  59      43 
59      28 
59      14 
59        0 
58      47 

Xll    .11      5 
12 
12     2 
12     3 

12      5 

All      13      57 
13      49 
13      41 
13      32 
,13      22 

XII     7      19 

7        0 
6     42 
6      23 
6        4 

XI  58      34 
58     22 
58      10 
57      58 
57     47 

26 
27 
28 

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13      2 
13     3 

13      4 

Xii     13      12 
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5      27 
5        8 

4      50 
4      31 

XI  57     37 
57     27 
57      17 
57        8 
57       0 

<!  31 

IJ      5 

4      ;3 

204 


Equation-Tables. 


A  TABLE  shewing  what  Time  it  ought  to  be  by  the 

Clock  when  the  Sun's  Centre  is  on  the  Meridian. 

The  third  Year  after  Leap-Year. 


o 

May. 

June. 

July. 

August.      S 

H        M.     S.H.       M.     S. 

M.    S.H      M    s    £ 

5 

XI       56     52 
56     45 
56     38 
56     32 
56      26 

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57     31 
57     41 
57      51 
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Xll     3     20 
3     31 
3     42 
3     53 

4       4 

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5      41   <J 
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56      17 

56      13 
56        9 
56        6 

XI       58      12 

58      23 
58      34 
58      45 
58      57 

XII     4      14 
4     24 
4      34 
4      43 
4      52 

XII  5      29  S 
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56        2 
56        1 
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5      22 
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56      20 
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0       4? 

Equation-  Tables. 


205 


TABLE  shewing  what  Time  it  ought  to  be  by  the' 
Clock  when  the  Sun's  Centre  is  on  the  Meridian. 
The  third  Year  after  Leap-Year. 


vl 

September. 

v  Jctober. 

November. 

December. 

li.       M.      :>. 

H.     M.     S. 

H.  BE  g; 

H.     M.     S. 

h 

2 

J     5 

XI       59      45 

59      26 
59        7 
58      48 
58      28 

XI    49      37 
49      19 
49        0 
48      42 
48      24 

XI    43     47 

43     47 
43     47 
43     47 
43     49 

XI     49      27 
49      50 
50      14 
50      38 
51        3 

>     6 

$     9 
S  10 

XI       58        9 

57     49 
57     28 
57        8 
56      47 

XI     48        7 
47      50 
47      33 
47      17 
47        1 

XI     43      52 
43      55 

43      59 
44        4 
44      10 

XI     51      29 
51      55 
52      21 
52      48 
53      15 

{- 

S  13 

$  14 
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55      45 
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55        3 

XI     46      46 
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XI     44      17 

44     25 
44     33 
44     43 
44      53 

XI     53      43 

54      11 
54     40 
55        8 
55      37 

XI       54      42 
54     20 
53      59 
53      38 
53      17 

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45      25 
45      14 
45        3 

44      53 

XI     45        4 

45      16 
45      29 
45      42 
45      57 

XI     56        7 

56      36 
57        6 
57      36 
58        6 

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52      36 
52      15 
51      55 
51      35 

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44      35 
44      27 
44      19 
44      13 

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46     28 
46     45 
47        3 
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59        6 
59     36 
XII     0        6 

0      36 

26 
$27 
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£  29 
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50      35 
50      15 
49      56 

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43      53 
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48        0 
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48     42 
49        4 

XII      1        6 

1      36 
2        6 
2      35 
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43      48 

3      34 

206 


*#*  OBSERVE  by  a  good  meridian-line,  or  by 
a  transit-instrument,  properly  fixed,  the  moment 
when  the  Sun's  centre  is  on  the  meridian;  and  set 
the  clock  to  the  time  marked  in  the  preceding 
table  for  that  day  of  the  year.  Then  if  the  clock 
goes  true,  it  will  point  to  the  time  shewn  in  the 
table  every  day  afterward  at  the  instant  when  it  is 
noon  by  the  Sun,  which  is  when  his  centre  is  on 
the  meridian. — Thus,  in  the  first  year  after  leap- 
year,  on  the  20th  of  October,  when  it  is  noon  by 
the  Sun,  the  true  equal  time  by  the  clock  is  only 
44  minutes  49  seconds  past  XI;  and  on  the  last 
day  of  December  (in  that  year)  it  should  be  3  mi- 
nutcs  47  seconds  past  XII  by  the  clock  when  the 
Sun's  centre  is  on  the  meridian. 

The  following  table  was  made  from  the  preced- 
ing one,  and  is  of  the  common  form  of  a  table  of 
the  equation  of  time,  shewing  how  much  a  clock 
regulated  to  keep  mean  or  equal  time  is  before 
or  behind  the  apparent  or  solar  time  every  day  of 
the  year. 


TABLE 


OF  THE 


EQUATION  OF  TIME, 


SHEWING 


How  much  a  Clock  should  be  faster  or  slower  than 
the  Sun,  at  the  Noon  of  every  Day  in  the  Year, 
both  in  Leap- Years  and  Common  Years. 


[  The  Asterisks  in  the  Table  shew  where  the  Equation 
changes  to  Slow  or  Fast.~\ 


Dd 


208 


Equation-  Tables. 


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S                  The  Bissextile,  or  Leap-Year  .                  «J 

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Equation-  Tables. 


209 


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Equation-  Tables. 


211 


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the  Moon's  /Y/f/v.  217 


CI1  \\\  XV. 

1'lie  J/<>''/r.v  Sur/licc  mountainous :  Her  Phases  de 
serihed:    Her  l\ith,   and  the    Paths  of  Jupiter's 
Moo'is  delineated:  The  Proportions  <>/  the  Diame- 
ters of  their  O/7;//.v,  and  those  of  Saturn's  Moons, 
to  each  other;  ami  the  Diameter  of  the  Sun. 


B 


1M.A    I   I.. 
VII. 


V  looking  at  the  MoonthroUffh  an  ordinary 
telescope,  \\e  perceive  that  her  surface  is 
diversified  \\  ilh  long ;  tracts  of  prodiglOUS high  mouil-  The 
tains  aiul  deep  cavities.   Some  of  her  mountains,  by  Moon's 
e-oinparinj;-  their  IK  i^ht  with  her  diameter  (which  laJJ^ 
2180  miles,)  are  ioimd  to  he  three-  times  as  high  as ou*. 
the  hi-hest  mountains  on  our  Ivmh.    This  rugged- 
ness  of  the  Moon's  surface  is  of  great  use  to  us,  by 
rdleeting  the  Sun's  light  to  all  sides:  for  if  the  Moon 
were  smooth  and  ])olished  like  a  looking- glass,  or  co- 
\t  red  with  water,  she  could  never  distribute  the  Sun's 
light  all  round:   only,  in  some  positions,  she  would 
shew  us  his  image-,  no  bigger  than  a  point,  but  with 
Mich  a  lustre  as  might  be  hurtful  to  our  e\ 

53«  The  Moon's  surface  being  so  uneven,  many 
have  wondered  why  her  edge  appears  not  jagged  as 
well  as  the  curve  bounding  the  light  and  dark  parts. 
But  if  we  consider,  that  what  we  call  the  edge  of  the  Why  no 
Moon's  disc  is  not  a  single  line  set  round  with  moun-  j^"*  JJJ" 
tains,  in  \\hich  case  it  would  appear  irregularly  in- her  edge 
dented,  but  a  large  zone,  having- many  mountains  ly- 
ing behind  one  another  from  the  observer's  eye,  we. 
shall  find  that  the  mountains  in  some  rows  will  be 
opposite  to  the  \ales  in  others,  and  fill  up  the  ine- 
qualities, so  as  to  make  her  appear  quite  round ; 
ju:,t  as  when  one  looks  at  an  orange,  although  its 
roughness  be  very  discernible  on  the  side  next  the 
eye,  especially  if  the  Sun  or  a  candle  shines  ob- 
liquely on  that  side,  yet  the  line  terminating  the  vi- 
sible part  still  appears  smooth  and  even. 


;>18  Of  the  Moon 's  Phase*. 


PLATE 
VII. 


254.  As  the  Sun  can  only  enlighten  that  half  of  the 
Earth  which  is  at  any  moment  turned  toward  him, 

The  Moon  and  being  withdrawn  from  the  opposite  half,  leaves  it 

twiU°ht  *n  darkness;  so  he  likewise  doth  to  the  Moon;  only 
with  this  difference,  that  the  Earth  being  surrounded 
by  an  atmospherer  and  the  Moon,  as  far  as  we  know, 
having  none,  we  have  twilight  after  the  Sun  sets; 
but  the  Lunar  inhabitants  have  an  immediate  transi- 
tion from  the  brightest  sunshine  to  the  blackest  dark- 
ness, §  177.  For,  let  t  r  k  s  w  be  the  Earth,  and  A* 
B,  C,  D,  E,  F,  G,  H,  the  Moon,  in  eight  different 

*"»£•  !•  parts  of  her  orbit.  As  the  Earth  turns  round  its 
axis,  from  west  to  east,  when  any  place  comes  to 
t,  the  twilight  begins  there,  and  when  it  revolves 
from  thence  to  r,  the  Sun  S  rises ;  when  the  place 
comes  to  s,  the  Sun  sets,  and  when  it  comes  to  iv, 
the  twilight  ends.  But  as  the  Moon  turns  round 
her  axis,  which  is  only  once  a  month,  the  moment 
that  any  point  of  her  surface  comes  to  r  (see  the 
Moon  at  G)  the  Sun  rises  there  without  any  pre- 
vious warning  by  twilight ;  and  when  the  same  point 
comes  to  5  the  Sun  sets,  and  that  point  goes  into 
darkness  as  black  as  at  midnight. 

The  ,          255.  The  Moon  beine:  an  opaque  spherical  body 

Moon's       /r       ,         u.n         ,          ir  r  iT  i 

phases.  (f°r  ner  O"*s  take  oft  no  more  from  her  roundness 
than  the  inequalities  on  the  surface  of  an  orange  take 
off  from  its  roundness),  we  can  only  see  that  part  of 
the  enlightened  half  of  her  which  is  toward  the  Earth. 
And  therefore  when  the  Moon  is  at  A,  in  conjunction 
with  the  Sun  £,  her  dark  half  is  toward  the  Earth, 
and  she  disappears,  as  at  a;  there  being  no  light  on 
that  half  to  render  it  visible.  When  she  comes  to 
her  first  octant  at  B,  or  has  gone  an  eighth  part  of 
her  orbit  from  her  conjunction,  a  quarter  of  her  en- 
lightened side  is  seen  toward  the  Earth,  and  she  ap- 
pears horned,  as  at  //.  When  she  has  gone  a  quarter 
of  her  orbit  from  between  the  Earth  and  Sun  to  Cf, 
she  shows  us  one  half  of  her  enlightened  side,  as  at 
c ;  and  we  say,  she  is  a  quarter  old.  At  D  she  is  in 
her  second  octant,  and  by  shewing  us  more  of  her 


Of  the  Moon's  Phases.  219 

enlightened  side  she  appears  gibbous,  as  at  d.  At 
E  her  whole  enlightened  side  is  toward  the  Earth, 
and  therefore  she  appears  round  as  at  e  ;  when  we  * 
say  it  is  full  Moon.  In  her  third  octant  at  F,  part 
of  her  dark  side  being  toward  the  Earth,  she  again 
appears  gibbous,  and  is  on  the  decrease,  as  at/;  At 
G  we  see  just  one  half  of  her  enlightened  side,  and 
she  appears  half- decreased,  or  in  her  third  quarter, 
as  at  g.  At  //we  only  see  a  quarter  of  her  enlight- 
ened side,  being  in  her  fourth  octant,  where  she  ap- 
pears horned,  as  at  h.  And  at  A,  having  completed 
her  course  from  the  Sun  to  the  Sun  again,  she  dis- 
appears; and  we  say,  it  is  new  Moon.  Thus,  in 
going  from  A  to  E,  the  Moon  seems  continually  to 
increase ;  and  in  going  from  E  to  A,  to  decrease  in 
the  same  proportion;  having  like  phases  at  equal 
distances  from  A  to  E  ;  but  as  seen  from  the  Sun 
S,  she  is  always  full. 

256.  The  Moon  appears  not  perfectly  round  when  The  t 
she  is  full  in  the  highest  or  lowest  part  of  her  orbit,  5S^Jt 
because  we  have  not  a  full  view  of  her  enlightened  always 
side  at  that  time.    When  full  in  the  highest  part  bfjjjjji 
her  orbit  a  small  deficiency  appears  on  her  lower  when  full, 
edge;  and  the  contrary,  when  full  in  the  lowest  part 

of  her  orbit. 

257.  It  is  plain  by  the  figure,  that  when  the  Moon  The  Pb»- 
changes  to  the  Earth,  the  Earth  appears  Ml  to  theE^jf 
Moon ;  and  vice  versa.     For  when  the  Moon  is  at  Moon  con- 
A,  new  to  the  Earth,  the  whole  enlightened  side  of trary> 
the  Earth  is  toward  the  Moon ;  and  when  the  Moon 

is  at  £,  full  to  the  Earth,  its  dark  side  is  toward  her. 
Hence  a  new  Moon  answers  to  -&full  Earth,  and  a 
full  Moon  to  a  new  Earth.  The  quarters  are  also 
reversed  to  each  other. 

258.  Between  the  third  quarter  and  change,  theAnagree- 
Moon  is  frequently  visible  in  the  forenoon,  even  when 

the  Sun  shines ;  and  then  she  affords  us  an  opportu- 
nity of  seeing  a  very  agreeable  appearance,  wherever 
we  find  a  globular  stone  above  the  level  of  the  eye, 


nomcnon. 


220  Of  the  Mootfs  Phases. 

as  suppose  on  the  top  of  a  gate.     For,  if  the  Sun 
shines  on  the  stone,  and  we  place  ourselves  so  as  the 
upper  part  of  the  stone  may  just  seem  to  touch  the 
point  of  the  Moon's  lowermost  horn,  we  shall  then 
see  the  enlightened  part  of  the  stone  exactly  of  the 
same  shape  with  the  Moon  ;  horned  as  she  is,  and 
inclined  in  the  same  way  to  the  horizon.    The  rea- 
son is  plain;  for  the  Sun  enlightens  the  stone  the 
same  way  as  he  does  the  Moon :  and  both  being 
globes,  when  we  put  ourselves  into  the  above  situ- 
ation, the  Moon  and  stone  have  the  same  position 
to  our  eye  ;  and  therefore  we  must  see  as  much  of 
the  illuminated  part  of  the  one  as  of  the  other. 
The  nona-     259.  The  position  of  the  Moon's  cusps,  or  a  right 
dee-reef     ^ne  touching  the  points  of  her  horns,  is  very  differ- 
ently  inclined  to  the  horizon  at  different  hours  of  the 
same  days  of  her  age.    Sometimes  she  stands,  as  it 
were,  upright  on  her  lowrer  horn,  and  then  such  a 
line  is  perpendicular  to  the  horizon ;  when  this  hap- 
pens, she  is  in  what  the  astronomers  call  the  nonage- 
simal  degree;  which  is  the  highest  point  of  the  eclip- 
tic above  the  horizon  at  that  time,  and  is  90  degrees 
from  both  sides  of  the  horizon,  where  it  is  then  cut 
by  the  ecliptic.     But  this  never  happens  when  the 
Moon  is  on  the  meridian,  except  when  she  is  at  the 
very  beginning  of  Cancer  or  Capricorn. 
HOW  the       260.  The  inclination  of  that  part  of  the  ecliptic  to 
inclination  fa  horizon  in  which  the  Moon  is  at  any  time  when 
ecliptic     horned,  may  be  known  by  the  position  of  her  horns; 
may  be     for  a  right  line  touching  their  points  is  perpendicu- 
thenpdosf-   lar  to  the  ecliptic.  And  as  the  angle  which  the  Moon's 
tion  of  the  orbit  makes  with  the  ecliptic  can  never  raise  her 
horns'8     ab°ve>  nor  depress  her  below  the  ecliptic,  more  than 
two  minutes  of  a  degree,  as  seen  from  the  Sun ;  it 
can  have  no  sensible  effect  upon  the  position  of  her 
horns.  Therefore,  if  a  quadrant  be  held  up,  so  as  that 
one  of  its  edges  may  seem  to  touch  the  Moon's  horns, 
the  graduated  side  being  kept  toward  the  eye,  and 
as  far  from  the  eye  as  it  can  be  conveniently  held,  the 


Of  the  Moon's  Phases.  221 


PLATE 
VII. 


arc  between  the  plumb-line  and  that  edge  of  the 
quadrant  which  seems  to  touch  the  Moon's  horns, 
will  shew  the  inclination  of  that  part  of  the  ecliptic 
to  the. horizon.  And  the  arc  between  the  other 
edge  of  the  quadrant  and  plumb-line,  will  shew  the 
inclination  of  a  line,  touching  the  Moon's  horns,  to 
the  horizon. 

261.  The  Moon  generally  appears  as  large  as  the  Fig.  i. 
Sun ;  for  the  angle  v  k  A^  under  which  the  Moon  is  why  the 
seen  from  the  Earth,  is  nearly  the  same  with  the  an-  ^ar"aT 
gle  LkM,  under  which  the  Sun  is  seen  from  it.  And  big  as  the 
therefore  the  Moon  may  hide  the  Sun's  whole  disc  Sun* 
from  us,  as  she  sometimes  does  in  solar  eclipses. 

The  reason  why  she  does  not  eclipse  the  Sun  at  eve- 
ry change,  shall  be  ex  plained  hereafter.  If  the  Moon 
were  farther  from  the  Earth,  as  at  c,  she  would  ne- 
ver hide  the  whole  of  the  Sun  from  us ;  for  then  she 
would  appear  under  the  angle  N k  O,  eclipsing  only 
that  part  of  the  Sun  which  lies  between  A*  and  O ; 
were  she  still  farther  from  the  Earth,  as  .at  X,  she 
would  appear  under  the  small  angle  T  k  W^  like  a 
spot  on  the  Sun,  hiding  only  the  part  y/iFfromour 
sight. 

262.  That  the  Moon  turns  round  her  axis  in  the  A  proof 
time  that  she  goes  round  her  orbit,  is  quite  demon-  of  ^ 
strable;  for  a  spectator  at  rest,  without  the  periphery  turning 
of  the  Moon's  orbit,  would  see  all  her  sides  turned  roi™i  her 
regularly  toward  him  in  that  time.  She  turns  round35 

her  axis  from  any  star  to  the  same  star  again  in  27 
days  8  hours ;  from  the  Sun  to  the  Sun  again,  in  29|. 
days  :  the  former  is  the  length  of  her  sidereal  day, 
and  the  latter  the  length  of  her  solar  day.  A  body 
moving  round  the  Sun  would  have  a  solar  day  in  eve- 
ry  revolution,  without  turning  on  its  axis;  the  same 
as  if  it  had  kept  all  the  while  at  rest,  and  the  Sun 
moved  round  it :  but  without  turning  round  its  axis 
it  could  never  have  one  sidereal  day,  because  it  would 
always  keep  the  same  side  toward  any  given  star. 


222 


An  easy  Way  of  representing 


revoiu- 


Her  perio-  263.  If  the  Earth  had  no  annual  motion,  the  Moon 
would  go  round  it  so  as  to  complete  a  lunation,  a  si- 
dereal,  and  a  solar  day,  all  in  the  same  time.  But 
because  the  Earth  goes  forward  in  its  orbit  while  the 
Moon  goes  round  the  Earth  in  her  orbit,  the  Moon 
must  go  as  much  more  than  round  her  orbit  from 
change  to  change  in  completing  a  solar  day,  as  the 
Earth  has  gone  forward  in  its  orbit  during  that  time, 
i.  e.  almost  a  twelfth  part  of  a  circle. 
Familiarly  264.  The  Moon's  periodical  and  sy  nodical  revo- 
represent-  \u^\on  may  be  familiarly  represented  by.  the  motions 
of  the  hour  and  minute-hands  of  a  watch  round  its 
dial-plate,  which.  is  divided  into  12  equal  parts  or 
hours,  as  the  ecliptic  is  divided  into  12  signs,  and 
the  year  into  12  months.  Let  us  suppose  these  12 
hours  to  be  12  signs,  the  hour-hand,  the  Sun,  and 
the  minute-hand,  the  Moon  ;  then  the  former  will  go 
round  once  in  a  year,  and  the  latter  once  in  a  month  : 
but  the  Moon,  or  minute-hand,  must  go  more  than 
round  from  any  point  of  the  circle  where  it  was  last 
conjoined  with  the  Sun,  or  hour-hand,  to  overtake  it 
again  :  for  the  hour-hand,  being  in  motion,  can  ne- 
ver be  overtakenby  theminute-handat  that  point  from 
which  they  started  at  their  last  conjunction.  The  first 


A  Table 
shewing 
the  times 
that  the 
hour  and 
minute- 
hands  of  a 
•watch  are 
in  con- 
junction. 


Conj. 

H. 

M. 

S. 

in 

"'•' 

vpts.'£ 

1 

1 

5 

27 

16 

21 

49.J-  £ 

2 

II 

10 

54 

32 

43 

38-JL  S 

3 

III 

16 

21 

49 

5 

27  s    S 

4 

IV 

21 

49 

5 

27 

16JL  S 

5 

V 

27 

10 

21 

49 

5-1 

6 

VI 

32 

43 

38 

10 

54  e     S 

7 

VII 

38 

10 

54 

32 

43V  § 

8 

VIII 

43 

38 

10 

54 

,«TT  J 
32_8_  } 

9 

IX 

49 

5 

27 

16 

21T91    ^ 

10 

X 

54 

32 

43 

38 

lOio  ? 

11 

XII 

0 

0 

0 

0 

o11  s 

Tire  Motion  of  the  Sun  and  Moon.  223 

column  of  the  preceding  table  shews  the  number  of : 


PLATE 
VII. 


conjunctions  which  the  hour  and  minute-hand  make 
while  the  hour-hand  goes  once  round  the  dial- plate ; 
and  the  other  columns  shew  the  times  when  the  two 
hands  meet  at  each  conjunction.  Thus,  suppose 
the  two  hands  to  be  in  conjunction  at  XII.  as  they 
always  are;  then  at  the  first  following  conjunction 
it  is  5  minutes  27  seconds  16  thirds  2i  fourths,  49^ 
fifths  past  I,  where  they  meet :  at  the  second  con- 
junction  it  is  10  minutes  54  seconds  32  thirds  43 
fourths  38^-  fifths  past  II ;  and  so  on.  This,  though 
an  easy  illustration  of  the  motions  of  the  Sun  and 
Moon,  is  not  precise  as  to  the  times  of  their  con- 
junctions; because,  while  the  Sun  goes  round  the 
ecliptic,  the  Moon  makes  12-|  conjunctions  with 
him;  but  the  minute-hand  of  a  watch  or  clock  makes 
only  11  conjunctions  with  the  hour-hand  in  one  pe- 
riod round  the  dial-plate.  But  if,  instead  of  the 
common  wheel- work  at  the  back  of  the  dial-plate, 
the  axis  of  the  minute-hand  had  a  pinion  of  6  leaves 
turning  a  wheel  of  74,  and  this  last  turning  the  hour- 
hand,  in  every  revolution  it  makes  round  the  dial- 
plate,  the  minute-hand  would  make  12-^  conjunc- 
tions with  it ;  and  so  would  be  a  pretty  device  for 
shewing  the  motions  of  the  Sun  and  Moon;  espe- 
cially, as  the  slowest  moving  hand  might  have  a  little 
sun  fixed  on  its  point,  and  the  quickest,  a  little 
moon. 

265.  If  the  Earth  had  no  annual  motion,  the  The 
Moon's  motion,  round  the  Earth,  and  her  track  in  Mo°n's 

,  ,    ,  T^,  motion 

open  space,  would  be  always  the  same.  *     But  as  through 
the   Earth   and  Moon  move  round  the  Sun,  the°Pens.pace 
Moon's  real  path  in  the  heavens  is  very  different  e"cl 
from  her  visible  path  round  the  Earth :  the  latter  be- 

*  In  this  place,  we  may  consider  the  orbits  of  all  the  satellites  as 
circular,  with  respect  to  their  primary  planets ;  because  the  eccen- 
tricities of  their  orbits  are  too  small  to  affect  the  phenomena  here 
described 

F   f 


224  The  Moods' Path  delineated. 


VII. 


PLATE  mg  in  a  progressive  circle,  and  the  former  in  a  curve 
of  different  degrees  of  concavity,  which  would  al- 
ways be  the  same  in  the  same  parts  of  the  heavens, 
if  the  Moon  performed  a  complete  number  of  luna- 
tions in  a  year,  without  any  fraction. 
An  idea  266.  Let  a  nail  in  the  end  of  the  axle  of  a  cha- 
jfarut's  n°t-wheel  represent  the  Earth,  and  a  pin  in  the  nave 
path,  and  the  Moon ;  if  the  body  of  the.  chariot  be  propped  up 
the  ,  so  as  to  keep  that  wheel  from  touching  the  ground, 
and  the  wheel  be  then  turned  round  by  hand,  the  pin 
will  describe  a  circle  both  round  the  nail  and  in  the 
space  it  moves  through.  But  if  the  props  be  taken 
away,  the  horses  put  to,  and  the  chariot  driven  over 
a  piece  of  ground  which  is  circularly  convex ;  the 
nail  in  the  axle  will  describe  a  circular  curve,  and 
the  pin  in  the  nave  will  still  describe  a  circle  round 
the  progressive  nail  in  the  axle,  but  not  in  the  space 
through  which  it  moves.  In  this  case  the  curve  de- 
scribed by  the  nail,  will  resemble,  in  miniature,  as 
much  of  the  Earth's  annual  path  round  the  Sun,  as 
it  describes  while  the  Moon  goes  as  often  round  the 
Earth  as  the  pin  does  round  the  nail :  and  the  curve 
described  by  the  nail  will  have  some  resemblance 
to  the  Moon's  path  during  so  many  lunations. 

Let  us  now  suppose  that  the  radius  of  the  circular 
curve  described  by  the  nail  in  the  axle  is  to  the  radi- 
us of  the  circle  which  the  pin  in  the  nave  describes 
round  the  axle  as  337-|-  to  1 ;  which  is  the  propor- 
tion of  the  radius  or  semi-diameter  of  the  Earth's 
orbit  to  that  of  the  Moon's  ;  or  of  the  circular  curve 
A  1  2  3  4  5  6  7  B,  &c.  to  the  little  circle  a;  and 
then  while  the  progressive  nail  describes  the  said 
curve  from  A  to  E,  the  pin  will  go  once  round  the 
nail  with  regard  to  the  centre  of  its  path,  and  in  so 
doing,  will  describe  the  curve  a  b  c  d  e.  The  for- 
mer will  be  a  true  representation  of  the  Earth's 
path  for  one  lunation,  and  the  latter  of  the  Moon's 
for  that  time.  Here  we  may  set  aside  the  inequali- 
ties of  the  Moon's  motion,  and  also  those  of  the 


The  Moon's  Path  delineated.  225 


|.    PLATE 
VII.    . 


Earth's  moving  round  their  common  centre  of  gra- 
vity :  all  which,  if  they  were  truly  copied  in  this 
experiment,  would  not  sensibly  alter  the  figure  of 
the  paths  described  by  the  nail  and  pin,  even  though 
they  should  rub  against  a  plane  upright  surface  all 
the  way,  and  leave  their  tracks  visibly  upon  it.  And 
if  the  chariot  were  driven  forward  on  such  a  con  vex 
piece  of  ground,  so  as  to  turn  the  wheel  several 
times  round,  the  track  of  the  pin  in  the  nave  would 
still  be  concave  toward  the  centre  of  the  circular 
curve  described  by  the  pin  in  the  axle :  as  the  Moon's 
path  is  always  concave  to  the  Sun  in  the  centre  of 
the  Earth's  annual  orbit. 

In  this  diagram,  the  thickest  curve- line  ABCDE, 
with  the  numeral  figures  set  to  it,    represents  as 
much  of  the  Earth's  annual  orbit  as  it  describes  in 
32  days  from  west  to  east ;  the  little  circles  at  «,  6, 
c,  d,  e,  shew  the  Moon's  orbit  in  due  proportion  to 
the  Earth's ;  and  the  smallest  curve  abed  e  f  re- 
presents the  line  of  the  Moon's  path  in  the  heavens 
for  32  days,   accounted  from  any  particular  new 
Moon  at  a.     The  machine  Fig.  5th,  is  for  deline- 
ating the  Moon's  path,  and  shall  be  described,  with 
the  rest  of  my  astronomical  machinery  in  the  last . 
chapter.     The  Sun  is  supposed  to  be  in  the  centre 
of  the  curve  A  \  2  3  4  5  6  7  B,  &c.  asd  the  small 
dotted  circles  upon  it,  represent  the  Moon's  orbit, 
of  which  the  radius  is  in  the  same  proportion  to  the  ^Pof the 
Earth's  path  in  this  scheme,  that  the  radius  of  the  Moon's 
Moon's  orbit  in  the  heavens  bears  to  the  radius  of ^il  to 
the  Earth's  annual  path  round  the  Sun :   that  is,  as  Earth's. 
240,000,  to  81,000,000*,  or  as  1  to  337|. 

When  the  Earth  is  at  A,  the  new  Moon  is  at  a  ; 
and  in  the  seven  days  that  the  Earth  describes  the 
curve  1234567,  the  Moon  in  accompanying  the  Fj&>  IL 
Earth  describes  the  curve  a  b ;  and  is  in  her  first 
quarter  at  b  when  the  Earth  is  at  B.     As  the  Earth 

*  For  the  true  distances,  see  p.  138. 


226  The  Moon's  Path  delineated. 


describes  the  curve  B  8  9  10  11  12  13  14,  the 
Moon  describes  the  curve  be;  and  is  at  c,  opposite 
to  the  Sun,  when  the  Earth  is  at  C.  While  the 
Earth  describes  the  curve  C  15  16  17  18  19  20  21 
22,  the  Moon  describes  the  curve  cd;  and  is  in  her 
third  quarter  at  d  when  the  Earth  is  at  D.  And  last- 
ly, while  the  Earth  describes  the  curve  D  23  24  25 
26  27  28  29,  the  Moon  describes  the  curve  de ; 
and  is  again  in  conjunction  at  e  with  the  Sun  when 
the  Earth  is  at  E,  between  the  29th  and  30th  day  of 
the  Moon's  age,  accounted  by  the  numeral  figures 
from  the  new  Moon  at  A.  In  describing  the  curve 
abode,  the  Moon  goes  round  the  progressive  Earth 
as  really  as  if  she  had  kept  in  the  dotted  circle  A, 
and  the  Earth  continued  immoveable  in  the  centre 
of  that  circle. 

The  ^          And  thus  we  see  that,  although  the  Moon  goes 

Motion  ai-  round  the  Earth  in  a  circle,  with  respect  to  the 

ways  con- Earth's  centre,  her  real  path  in  the  heavens  is  not 

warVthe  vei^  different  m  appearance  from  the  Earth's  path. 

Sun.         To  shew  that  the  Moon's  path  is  concave  to  the 

Sun,  even  at  the  time  of  change,  it  is  carried  on  a 

little  farther  into  a  second  lunation,  as  tof. 

267.  The  Moon's  absolute  motion  from  her  change 
to  her  first   quarter,  or  from  a  to  6,  is  so  much 
slower  than  the  Earth's,  that  she  falls  240  thousand 
miles  (equal  to  the  semi-diameter  of  her  orbit)  be- 
hind the  Earth  at  her  first  quarter  in  6,  when  the 
Earth  is  at  B ;  that  is,  she  falls  back  a  space  equal 
HOW  her  to  her  distance  from  the  Earth.    From  that  time  her 
is  alter      mot*on  *s  gradually  accelerated  to  her  opposition  or 
nateiyre-  full  at  c,  and  then  she  is  come  upas  far  as  the  Earth, 
!cctidrand  k^g  regained  what  she  lost  in  her  first  quarter 
C<L  e '     "  from  a  to  b.     From  the  full  to  the  last  quarter  at  d, 
her  motion  continues  accelerated,  so  as  to  be  just  as 
far  before  the  Earth  at  d,  as  she  was  behind  it  at  her 
first  quarter  in  b.     But  from  d  to  e  her  motion  is  re- 
tarded, so  that  she  loses  as  much  with  respect  to 
the  Earth  as  is  equal  to  her  distance  from  it,  or  to 
the  semi-diameter  of  her  orbit ;  and  by  that  means 


The  Moons  Path,  delineated.  227 


PLATE 
VII. 


she  comes  to  e,  and  is  then  in  conjunction  with  the 
Sun  as  seen  from  the  Earth  at  E.  Hence  we  find, 
that  the  Moon's  absolute  motion  is  slower  than  the 
Earth's  from  her  third  quarter  to  her  first ;  and  swift- 
er than  the  Earth's  from  her  first  quarter  to  her 
third ,  her  path  being  less  curved  than  the  Earth's 
in  the  former  case,  and  more  in  the  latter.  Yet  it  is 
still  bent  the  same  way  toward  the  Sun  ;  for  if  we 
imagine  the  concavity  of  the  Earth's  orbit  to  be 
measured  by  the  length  of  a  perpendicular  line  Cg, 
let  down  from  the  Earth's  place  upon  the  straight 
line  bgd  at  the  full  of  the  Moon,  and  connecting 
the  places  of  the  Earth  at  the  end  of  the  Moon's 
first  and  third  quarters,  that  length  will  be  about  640 
thousand  miles  ;  and  the  Moon  when  new  only  ap- 
proaching nearer  to  the  Sun  by  240  thousand  miles 
than  the  Earth,  is  the  length  of  the  perpendicular 
let  down  from  her  place  at  that  time  upon  the  same 
straight  line,  all  which  shews  that  the  concavity  of 
that  part  of  her  path,  will  be  about  400  thousand 
miles. 

26€.  The  Moon's  path  being  concave  to  the  Sun  A  difficuK 
throughout,  demonstrates  that  her  gravity  toward  *? remov- 
the  Sun  at  her  conjunction,  exceeds  her  gravity  to- tc 
ward  the  Earth.  And  if  we  consider  that  the  quan- 
tity of  matter  in  the  Sun  is  almost  230  thousand 
times  as  great  as  the  quantity  of  matter  in  the  Earth, 
and  that  the  attraction  of  each  body  diminishes  as 
the  square  of  the  distance  from  it  increases,  we  shall 
soon  find,  that  the  point  of  equal  attraction  between 
the  Earth  and  the  Sun,  is  about  70  thousand  miles 
nearer  the  Earth  than  the  Moon  is  at  her  change. 
It  may  then  appear  surprising  that  the  Moon  does 
not  abandon  the  Earth,  when  she  is  between  it  and 
the  Sun,  because  she  is  considerably  more  attract- 
ed  by  the  Sun  than  by  the  Earth  at  that  time. 
But  this  difficulty  vanishes  when  we  consider,  that 
a  common  impulse  on  any  system  of  bodies  aftecfe 


228  The  Reason  why  the  Moon  does  not 

PLATE  not  their  relative  motions;  but  that  they  will  conti- 
nue to  attract,  impel,  or  circulate  round  one  another, 
in  the  same  manner  as  if  there  were  no  such  impulse. 
The  Moon  is  so  near  the  Earth,  and  both  of  them 
so  far  from  the  Sun,  that  the  attractive  power  of  the 
Sun  may  be  considered  as  equal  on  both :  and  there- 
fore the  Moon  will  continue  to  circulate  round  the 
Earth  nearly  in  the  same  manner  as  if  the  Sun  did 
not  attract  them  at  all.  For  bodies  in  the  cabin  of  a 
ship,  may  move  round,  or  impel  one  another  in  the 
same  manner  when  the  ship  is  under  sail,  as  when 
it  is  at  rest ;  because  they  are  all  equally  affected  by 
the  common  motion  of  the  ship.  If  by  any  other 
cause,  such  as  the  near  approach  of  a  comet,  the 
Moon's  distance  from  the  Earth  should  happen  to 
be  so  much  increased,  that  the  difference  of  their 
gravitating  forces  toward  the  Sun  should  exceed 
that  of  the  Moon  toward  the  Earth ;  in  that  case 
the  Moon  when  in  conjunction,  would  abandon  the 
Earth,  and  be  either  drawn  into  the  Sun  or  comet, 
or  circulate  round  about  it. 

Fig.  in.  269.  The  curves  which  Jupiter's  satellites  de- 
scribe, are  all  of  different  sorts  from  the  path  describ- 
ed by  our  Moon,  although  these  satellites  go  round 
Jupiter  as  the  Moon  goes  round  the  Earth.  Let 
ABCDE,  &c.  be  as  'much  of  Jupiter's  orbit  as  he 
describes  in  18  days  from  A  to  T ';  and  the  curves 
a,  6,  c,  dj  will  be  the  paths  of  his  four  moons  going 
round  him  in  his  progressive  motion. 

The  abso-     Now  let  us  suppose  all  these  moons  to  set  out 
of^uptter  fr°m  a  conjunction  with  the  Sun,  as  seen  from  Jupi- 
and  his     ter  at  A  ;  then  his  first  or  nearest  moon  will  be  at  c, 
ddLtoeat!   ^s  seconc^  at  &>  ^s  *h\rd  at  c,  and  his  fourth  at  d. 
ed.          At  the  end  of  24  terrestrial  hours  after  this  conjunc- 
tion, Jupiter  has  moved  to  £,  his.  first  moon  or  sa* 
tellite  has  described  the  curve  a  1,  his  second  the 
curve  b  1,  his  third  c  1,  and  his  fourth  d  1.     The 
next  day,  when  Jupiter  is  at  C,  his  first  satellite  has 


abandon  the  Earth  at  the  Time  of  her  Change.  229 

described  the  curve  a  2,  from  its  conjunction,  hisPI^E 
second  the  curve  b  2,  his  third  the  curve  c  2,  and 
his  fourth  the  curve  d  2,  and  so  on.  The  numeral 
figures  under  the  capital  letters  shew  Jupiter's  place 
in  his  path  every  day  for  18  days,  accounted  from 
A  to  T;  and  the  like  figures  set  to  the  paths  of  his 
satellites,  shew  where  they  are  at  the  like  times. 
The  first  satellite,  almost  under  C,  is  stationary  at 
-f,  as  seen  from  the  Sun;  and  retrograde  from  -f 
to  2 :  at  2  it  appears  stationary  again,  and  thence  it 
moves  forward  until  it  has  passed  3,  and  is  twice 
stationary  and  once  retrograde  between  3  and  4. — 
The  path  of  this  satellite  intersects  itself  every  42£ 
hours,  making  such  loops  as  in  the  diagram  at  2.  3. 
5.  7.  9.  10.  12.  14.  16.  18,  a  little  after  every 
conjunction.  The  second  satellite  £,  moving  slow- 
er, barely  crosses  its  path  every  3  clays  13  hours; 
as  at  4.  7.  11.  14,  18.  making  only  5  loops  and  as 
many  conjunctions  in  the  time  that  the  first  makes 
ten.  The  third  satellite  c,  moving  still  slower,  and 
having  described  the  curve  c  1.  2.  3.  4.  5.  6.  7, 
comes  to  an  angle  at  7,  in  conjunction  with  the  Sun, 
at  the  end  of  7  days  4  hours ;  and  so  goes  on  to 
describe  such  another  curve  7.  8.  9.  10.  11.  12. 
13.  14,  and  is  at  14  in  its  next  conjunction. 
The  fourth  satellite  d  is  always  progressive,  mak- 
ing neither  loops  nor  angles  in  the  heavens ; 
but  comes  to  its  next  conjunction  at  e  between  Flff' IIL 
the  numeral  figures  16  and  17,  or  in  16  days  18 
hours.  In  order  to  have  a  tolerable  good  figure  of  the 
paths  of  these  satellites,  I  took  the  following  method. 
Having  drawn  their  orbits  on  a  card,  in  propor- 
tion to  their  relative  distances  from  Jupiter,  I  mea-  Fig.  iv. 
sured  the  radius  of  the  orbit  of  the  fourth  satellite, 
which  was  an  inch  and  /^  parts  of  an  inch  ;  then 
multiplied  this  by  424  for  the  radius  of  Jupiter's 
orbit,  because  Jupiter  is  424  times  as  far  from  the 
Sun's  centre  as  his  fourth  satellite  is  from  his  cen- 
tre, and  the  product  thence  arising  was  483 -^ 


230  The  Paths  of  Jupiter's  Moons  delineated. 

PLATE     i,lches.     Then  taking  a  small  cord  of  this  length, 


and  fixing  one  end  of  it  to  the  floor  of  a  long  room 
to     by  a  nail,  with  a  black-lead  pencil  at  the  other  end 

*  drew  llie  Clirve  •^CA  &c.  and  set  off  a  degree 
and  a  half  thereon,  from  A  to  T  ;  because  Jupiter 
ter's  moves  only  so  much,  while  his  outermost  satellite 
>ns'  goes  once  round  him,  and  somewhat  more  :  so  thai 
this  small  portion  of  so  large  a  circle  differs  but  ve- 
ry little  from  a  straight  line.  This  done  I  divided 
the  space  A  T'mto  18  equal  parts,  as  A  B,  B  C, 
&c.  for  the  daily  progress  of  Jupiter  ;  and  each 
part  into  24  for  his  hourly  progress.  The  orbit  of 
each  satellite  was  also  divided  into  as  many  equal 
parts  as  the  satellite  is  hours  in  finishing  its  synodi- 
cal  period  round  Jupiter.  Then  drawing  a  right 
line  through  the  centre  of  the  card,  as  a  diameter 
to  all  the  four  orbits  upon  it,  I  put  the  card  upon 
the  line  of  Jupiter's  motion,  and  transferred  it  to  ev- 
ery horary  division  thereon,  keeping  always  the 
same  diameter-  line  on  the  line  of  Jupiter's  path  ;  and 
running  a  pin  through  each  horary  division  in  the 
orbit  of  each  satellite  as  the  card  was  gradually  trans- 
ferred along  the  line  ABCD,  &c.  of  Jupiter's  mo- 
tion, I  marked  points  for  every  hour  through  the 
card  for  the  curves  described  by  the  satellites,  as 
the  primary  planet  in  the  centre  of  the  card  was  car- 
ried forward  on  the  line  ;  and  so  finished  the  figure, 
by  drawing  the  lines  of  each  satellite's  motion  through 
those  (almost  innumerable)  points  :  by  which  means, 
and  Sa  ^s  *s>  Pernaps,  as  true  a  figure  of  the  paths  of  these 
turn's.*"  satellites  as  can  be  desired.  And  in  the  same  man- 
ner might  those  of  Saturn's  satellites  be  delineated. 
The  grand  270.  It  appears  by  the  scheme,  that  the  three  first 
periods^of  satellites  come  almost  into  the  same  line  of  position 
moons!"  S  every  seventh  day  ;  the  first  being  only  a  little  behind 
with  the  second,  and  the  second  behind  with  the 
3d.  But  the  period  of  the  4th  satellite  is  so  incommen- 
surate to  the  periods  of  the  other  three,  that  it  cannot 


The  Pat/is  of  Jupiter's  Moons  delineated.  231 


PLATE 
VII. 


be  guessed  at  by  the  diagram  when  it  would  fall 
again  into  a  line  of  conjunction  with  them  between 
Jupiter  and  the  Sun.  And  no  wonder;  for  suppos- 
ing them  all  to  have  been  once  in  conjunction,  it  \\  ill 
require  3,087,043,493,260  years  to  bring  them  in 
conjunction  again.  See  §  73. 

271.  In  Fig.  4th,  we  have  the  proportions  of  the  Fig.  IV. 
orbits  of  Saturn's  five  satellites,  and  of  Jupiter's  four,  ™?.pro"  f 

-»  «-  t*  iii*       portions  ox 

to  one  another,  to  our  Moon's  orbit,  and  to  the  disc  the  orbits 
of  the  Sun.     S  is  the  Sun ;   M  m  the  Moon's  orbit  Jj™^** 
(the  Earth  supposed  to  be  at  E);  /Jupiter  j   1.  2.  satellites, 
3.  4,  the  orbits  of  his  four  moons  or  satellites;  Sat. 
Saturn ;  and  1.  2.  3.4.  5,  the  orbits  of  his  five 
moons.  Hence  it  appears,  that  the  Sun  would  much 
more  than  fill  the  whole  orbit  of  the  Moon  ;  for  the 
Sun's  diameter  is  763,000  miles,  and  the  diameter 
of  the  Moon's  orbit  only  480,000.  In  proportion  to 
all  these  orbits  of  the  satellites,  the  radius  of  Saturn's 
annual  orbit  would  be  2U  yards,  of  Jupiter's  orbit 
11§,  and  of  the  Earth's  2i,  taking  them  in  round 
numbers. 

272.  The  annexed  table  shews  at  once  what  pro- 
portion the  orbits,  revolutions,  and  velocities  of  all 
the  satellites  bear  to  those  of  their  primary  planets, 
and  what  sort  of  curves  the  several  satellites  describe. 
For  those  satellites,  whose  velocities  round  their  pri- 
maries are  greater  than  the  velocities  of  their  prima- 
ries in  open  space,  make  loops  at  their  conjunctions, 
5  269 ;  appearing  retrograde  as  seen  from  the  Sun 
svhile  they  describe  the  inferior  parts  of  their  orbits, 
and  direct  while  they  describe  the  superior.  This  is 
the  case  with  Jupiter's  first  and  second  satellites,  and 
with  Saturn's  first.  But  those  satellites,  whose  velo- 
cities are  less  than  the  velocities  of  their  primary  pla- 
nets, move  direct  in  their  whole  circumvolutions  ; 
which  is  the  case  of  the  third  and  fourth  satellites  of 
Jupiter,  and  of  the  second,  third,  fourth,  and  fifth 
satellites  of  Saturn,  as  well  as  of  our  satellite  the 
Moon :  but  the  Moon  is  the  only  satellite  whose 
motion  is  always  concave  to  the  Sun. 

Gg 


232  The  Curves  described  by  the  secondary  Planets. 


The 
Satellites 

Proportion    of 
the  Radius  of 
thePlanet'sOr- 
bit  to  the  Ra- 
dius of  the  Or- 
bit  of  each  Sa- 
tellite. 

Proportion    of 
the    Time    of 
the     Planet's 
Revolution   to 
the  Revolution 
of  each  Satel- 
lite. 

Proportion     ofS 
the  Velocity  of? 
each     Satellite  S 
to  the  Velocity  <J 
of  its  primary  S 
Planet.                £ 

$ 

5  °    l 

1 

As  5322  to  1 
4155         1 
2954 
1295 
432 

As  5738  to 
3912 
2347 
674 
134 

As5738to5322  S 
3912     4155  ^ 
2347     2954  S 
674      1295  § 
134       432  S 

$8,1 
1*1.  3 

As    1851   to 
1165 
731 
424 

As  2445  to 
1219 
604 
258 

As  2445  to  1851  S 
1219      1165J; 
604       731  S 
258       424  !j 

S    MOOQ 

As  337|  to   1 

As       12|  to   1 

As    12.Jto337|!j 

There  is  a  table  of  this  sort  in  De  la  Cattle's  As- 
tronomy, but  it  is  very  different  from  the  above, 
which  1  have  computed  from  our  English  accounts 
of  the  periods  and  distances  of  these  planets  and 
satellites. 


Of  the  Harvest-Moon.  233 


CHAP.  XVL 

The  Phenomena  of  the  Harvest-Moon  explained  by 
a  common  Globe.  The  Years  in  which  the  Har- 
vest Moons  are  least  and  most  beneficialfrom  1751 
to  1861.  The  long  Duration  of  Moon-light  at  the 
Poles  in  Winter. 


T 

J[ 


T  is  generally  believed  that  the  Moon  rises  No 
about  50  minutes  later  every  clay  than  on^s 
the  preceding  :  but  this  is  true  only  \vith  regard  to  equator: 
places  on  the  equator.  In  places  of  considerable 
latitude  there  is  a  remarkable  difference,  especially 
in  the  harvest  time,  with  which  farmers  were  better 
acquainted  than  astronomers,  till  of  late  ;  and 
gratefully  ascribed  the  early  rising  of  the  full  moon 
at  that  time  of  the  year  to  the  goodness  of  God,  not 
doubting  that  he  had  ordered  it  so  on  purpose  to 
give  them  an  immediate  supply  of  moon-light  after 
sun-  set,  for  their  greater  conveniency  in  reaping  the 
fruits  of  the  Earth. 

In  this  instance  of  the  harvest-moon,  as  in  many 
others  discoverable  by  astronomy,  the  wisdom  and 
beneficence  of  the  Deity  is  conspicuous,  who  really 
ordered  the  course  of  the  Moon  so,  as  to  bestow 
more  or  less  light  on  all  parts  of  the  Earth  as  their 
several  circumstances  and  seasons  render  it  more  or 
less  serviceable.  About  the  equator,  where  there  is 
no  variety  of  seasons,  and  the  weather  changes  sel- 
dom, and  at  stated  times,  moon-light  is  not  neces- 
sary for  gathering  in  the  produce  of  the  ground;  and 
there  the  Moon  rises  about  50  minutes  later  every 
day  or  night  lhan  on  the  former.  At  considerable 
distances  from  the  equator,  where  the  weather  and 
seasons  are  more  uncertain,  the  autumnal  full  Moon 
rises  very  soon  after  sun-set  for  several  evenings  to 


234  Of  the  Harvest-Moon. 

But  re-     gether.  At  the  polar  circles,  where  the  mild  season 
Scm-dine  *s  °^  very  s^ort  duration,  tne  autumnal  full  Moon 
to  the  dis.  rises  at  sun-set  from  the  first  to  the  third  quarter. 
tances  of  And  at  the  poles,  where  the  Sun  is  for  half  a  year 
from  it.     absent,  the  winter  full  Moons  shine  constantly  with- 
out setting  from  the  first  to  the  third  quarter. 
The  rea-        It  is  soon  said  that  all  these  phenomena  are  owing 
lis'to  the  different  angles  made  by  the  horizon  and  dif- 
ferent parts  of  the  Moon's  orbit ;  and  that  the  Moon 
can  be  full  but  once  or  twice  in  a  year  in  those  parts 
of  her  orbit  which  rise  with  the  least  angles.     But 
to  explain  this  subject  intelligibly,  we  must  dwell 
much  longer  upon  it. 

274.  The*  plane  of  the  equinoctial  is  perpendi- 
cular to  the  Earth's  axis ;  and  therefore,  as  the  Earth 
turns  round  its  axis,  all  parts  of  the  equinoctial  make 
equal  angles  with  the  horizon  both  at  rising  and  set- 
ting ;  so  that  equal  portions  of  it  always  rise  or  set 
in  equal  times.  Consequently,  if  the  Moon's  mo- 
tion were  equable,  and  in  the  equinoctial,  at  the  rate 
of  12  degrees  11  min.  from  the  Sun  every  day,  as 
it  is  in  her  orbit,  she  would  rise  and  set  50  minutes 
later  every  day  than  on  the  preceding ;  for  12  deg. 
11  min.  of  the  equinoctial*  rise  or  set  in  50  minutes 
of  time  in  all  latitudes. 

275.  But  the  Moon's  motion  is  so  nearly  in  the 
ecliptic,  that  we  may  consider  her  at  present  as 
moving  in  it.  Now  the  different  parts  of  the  eclip- 
tic, on  account  of  its  obliquity  to  the  Earth's  axis, 
make  very  different  angles  with  the  horizon  as  they 
rise  or  set.  Those  parts  or  signs  which  rise  with 
the  smallest  angles  set  with  the  greatest,  and  vice 
versa.  In  equal  times,  whenever  this  angle  is  least, 
a  greater  portion  of  the  ecliptic  rises  than  when  the 
angle  is  larger ;  as  may  be  seen  by  elevating  the 
pole  of  a  globe  to  any  considerable  latitude,  and  then 

*  If  a  globe  be  cut  quite  through  upon  any  circle,  the  flat 
surface  where  it  is  so  divided  is  the  plane  of  that  circle. 


Of  the  Harvest-Moon.  235 


turning  it  round  its  axis.     Consequently,  when  the 
Moon*  is  in  those  signs  which  rise  or  set  with  the 
smallest  angles,  she  rises  or  sets  with  the  least  dif- 
ference of  time  ;  and  with  the  greatest  difference  in  Fig.  HI. 
those  signs  which  rise  or  set  with  the  greatest  angles. 

But,  because  all  who  read  this  treatise  may  not 
be  provided  with  globes,  though  in  this  case  it  is  re- 
quisite to  know  how  to  use  them,  we  shall  substi- 
tute the  figure  of  a  globe;  in  which  FU  P  is  the 
axis,  25  TR  the  tropic  of  Cancer,  Lt  itf  the  tropic 
of  Capricorn,  22  E  U  >5  the  ecliptic  touching  both 
the  tropics,  which  are  47  degrees  from  each  other, 
and.^fjftthe  horizon.     The  equator  being  in  the 
middle  between  the  tropics,  is  cut  by  the  ecliptic  in 
two  opposite  points,  which  are  the  beginnings  of  v 
Aries  and  =^  Libra  ;  K  is  the  hour-circle  with  its 
index,  F  the  north  pole  of  the  globe  elevated  to  a 
considerable  latitude,  suppose  40  degrees  above  the 
horizon  ;  and  P  the  south  pole  depressed  as  much  Fis.  HI, 
below  it.     Because  of  the  oblique  position  of  the 
sphere  in  this  latitude,  the  eeliptic  has  the  high  ele- 
vation N  25  above  the  horizon,  making  the  angle  The  differ- 
AT/25  of  73£  degrees  with  it  when  25  Cancer  is  on^d^es 
the  meridian,  at  which  time  =2=  Libra  rises  in  the  the  eciip- 
east.  But  let  the  globe  be  turned  half  round  its  axis,  Hc  and  ho* 
till  >5  Capricorn  comes  to  the  meridian  and  <v*  Aries  l' 
rises  in  the  east,  and  then  the  ecliptic  will  have 
the  low  elevation  NL  above  the  horizon,  making 
only  an  angle  NUL  of  26J  degrees  with  it;  which 
is  47  degrees  less  than  the  former  angle,  equal  to 
the  distance  between  the  tropics. 

276.    In  northern  latitudes,  the  smallest  angle  Least  and 
made  by  the  ecliptic  and  horizon  is  when  Aries  rises, 
at  which  time  Libra  sets  ;  the  greatest  when  Libra 
rises,  at  which  time  Aries  sets.   From  the  rising  of 
Aries  to  the  rising  of  Libra  (which  is  twelve*  side- 

*  The  ecliptic,  together  with  the  fixed  stars,  make  366J 
apparent  diurnal  revolutions  about  the  Earth  in  a  year  ;  the 
Sun  only  3651.  Therefore  the  stars  gain  3  minutes  56  se« 


236 


Of  the  Haw est- Moon.. 


ral  hours)  the  angle  increases ;  and  from  the  rising 

of  Libra  to  the  rising  of  Aries,  it  decreases  in  the 

same  proportion.    By  this  article  and  the  preceding 

it  appears  that  the  ecliptic  rises  fastest  about  Aries, 

and  slowest  about  Libra. 

Result  of       277.  On  the  parallel  of  London,  as  much  of  the 
the  quan-  ecliptic  rises  about  Pisces  " 
angifat"8  an(^  Aries  in  two  hours  as  ? 
London,    the  Moon  goes  through  in  s 

six   days :    and    therefore  Jj 

while  the  Moon  is  in  these  ^ 

signs,  she  differs  but  two  S 

hours  in  rising  for  six  days  s 

together;  that  is,  about  20  \ 

minutes  later  every  day  or  !j 

night  than  on  the  preced- 1* 

ing,  at  a  mean  rate.     But  Jj 

in  fourteen  days  afterward,  S    9 

the  Moon  comes  to  Virgo 

and  Libra,  which  are  the 

opposite   signs   to  Pisces \  is 

and  Aries;  and  then  shejj  14 

differs  almost  four  times  as  S  J* 

much  in  rising;   namely,  s  17 

one  hour  and  about  fifteen  s  1 8 

minutes  later  every  day  or  s  19 

night  than  the  former,  while ' 

she  is  in  these  signs.  The  ^  ^ 

annexed  table  shews  the  s  33 

daily  mean  difference  of 

the  Moon's  rising  and  set- 
ting on  the  parallel  ofLo?i- 

don,  for  28  days;  in  which 

time  the  moon  finishes  her. 


1 

C/! 

^    <? 
3i      3 

Rising 
Diff.' 

Setting  S 
Diff.    s 

<t 

y. 

H.    M. 

H.    M.  ^ 

1 

25    13 

5 

0        50  £ 

2 

26 

10 

0        43  S 

3 

a  10 

14 

0       37  Jj 

4 

23 

17 

0        32  S 

5 

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conds  upon  the  Sun  every  day ;  so  that  a  sideral  day  con- 
tains only  23  hours  56  minutes  of  mean  solar  time  ;  and  a 
natural  or  solar  day  24  hours.  Hence  12  sideral  hours  are 
one  minute  58  seconds  shorter  than  12  solur  hours. 


Of  the  Harvest-Moon.  237 


PLATE 
III. 


period  round  the  ecliptic,  and  gets  9  degrees  into 
the  same  sign  from  the  beginning  of  which  she  set 
out.  Thus  it  appears  by  the  table,that  when  the  Moon 
is  in  *%  and  =&  she  rises  an  hour  and  a  quarter  later 
every  day  than  she  rose  on  the  former ;  and  differs 
only  28,  24,  20,  18  or  17  minutes  in  setting.  But, 
when  she  comes  to  X  and  V,  she  is  only  20  or  17 
minutes  later  in  rising ;  and  an  hour  and  a  quarter 
later  in  setting. 

278.  All  these  things  will  be  made  plain  by  put- 
ting small  patches  on  the  ecliptic  of  a  globe,  as  far 
from  one  another  as  the  Moon  moves  from  any  point 
of  the  celestial  ecliptic  in  24  hours,  which  at  a  mean 
rate  is*  13j  degrees;  and  then,  in  turning  the  globe 
round,  observe  the  rising  and  setting  of  the  patches 
in  the  horizon,  as  the  index  points  out  the  different 
times  on  the  hour-circle.  A  few  of  these  patches  are 
represented  by  dots  at  0  1  2  3,  &c.  on  the  ecliptic,  Fig.  ni 
which  has  the  position  Z/£7/when  Aries  rises  in  the 

east ;  and  by  the  dots  0123,  &x.  when  Libra  rises 
in  the  east,  at  which  time  the  ecliptic  has  the  posi- 
tion EUv3  :  making  an  angle  of  62  degrees  with 
the  horizon  in  the  latter  case,  and  an  angle  of  no 
more  than  15  degrees  with  it  in  the  former ;  suppos- 
ing the  globe  rectified  to  the  latitude  of  London. 

279.  Having  rectified  the  globe,  turn  it  until  the 
patch  at  0,  about  the  beginning  of  x  Pisces  in  the 
half  LUI  Q£  the  ecliptic,  comes  to  the  eastern  side 
of  the  horizon;  and  then,  keeping  the  ball  steady, 
set  the  hour-index  to  XII,  because  that  hour  may 
perhaps  be  more  easily  remembered  than  any  other. 
Then  turn  the  globe  round  westward,  and  in  that 
time,  suppose  the  patch  0  to'  have  moved  thence- 


*  The  Sun  advances  almost  a  degree  in  the  ecliptic  in  24 
hours,  the  same  way  that  the  Moon  moves ;  and  therefore 
the  Moon  by  advancing  13£  degrees  in  that  time,  goes  lit- 
tle more  than  12  degrees  farther  from  the  Sun  than  she  was 
on  the  day  before. 


238  Of  the  Harvest-Moon. 

to  1, 13 J  degrees,  while  the  Earth  turns  once  round 
its  axis,  and  you  will  see  that  1  rises  only  about  20 
minutes  later  than  0  did  on  the  day  before.  Turn 
the  globe  round  again,  and  in  that  time  suppose  the 
same  patch  to  have  moved  from  1  to  2 ;  and  it  will 
rise  only  20  minutes  later  by  the  hour- index  than 
it  did  at  1  on  the  day  or  turn  before.  At  the  end  of 
the  next  turn  suppose  the  patch  to  have  gone  from 
2  to  3  at  £7,  and  it  will  rise  20  minutes  later  than  it 
did  at  2,  and  so  on  for  six  turns,  in  which  time  there 
will  scarce  be  two  hours  difference ;  nor  would  there 
have  been  so  much,  if  the  6  degrees  of  the  Sun's 
motion  in  that  time  had  been  allowed  for.  At  the 
first  turn  the  patch  rises  south  of  the  east,  at  the 
middle  turn  due  east,  and  at  the  last  turn  north  of  the 
east.  But  these  patches  will  be  9  hours  in  setting 
on  the  western  side  of  the  horizon,  which  shews  that 
the  Moon's  setting  will  be  so  much  retarded  in  that 
week  in  which  she  moves  through  these  two  signs. 
The  cause  of  this  difference  is  evident ;  for  Pisces 
and  Aries  make  only  an  angle  of  15  degrees  with 
the  horizon  when  they  rise ;  but  they  make  an  angle 
of  62  degrees  with  it  when  they  set.  As  the  signs 
Taurus,  Gemini,  Cancer,  Leo,  Virgo,  and  Libra, 
rise  successively,  the  angle  increases  gradually  which 
they  make  with  the  horizon,  and  decreases  in  the 
same  proportion  as  they  set.  And  for  that  reason, 
the  Moon  differs  gradually  more  in  the  time  of  her 
rising  every  day  while  she  is  in  these  signs,  and  less 
in  her  setting :  after  which,  through  the  other  six 
signs,  viz.  Scorpio,  Sagittary,  Capricorn,  Aquarius, 
Pisces,  and  Aries,  the  rising-difference  becomes 
less  every  day,  until  it  be  at  the  least  of  all,  namely, 
in  Pisces  and  Aries. 

280.  The  Moon  goes  round  the  ecliptic  in  27 
days  8  hours :  but  not  from  change  to  change  in  less 
than  29  days  12  hours :  so  that  she  is  in  Pisces  and 
Aries  at  least  once  in  every  lunation,  and  in  some 
lunations  twice. 


Of  the  Hai~vest-MooK.  239 

281.   If  the  Earth  had  no  annual  motion,  the  why  the 
:Sun  would  never  appear  to  shift  his  place  in  the  *j£°ysis 
ecliptic.     And  then  every  new  Moon  would  fall  in  full  in  dif- 
the  samesign  and  degree  of  the  ecliptic,  and  every  ^?r^t 
full  Moon  in  the  opposite:  for  the  Moon  would  go  b'&ns 
precisely  round  the  ecliptic  from  change  to  change. 
-So  that  if  the  Moon  were  once  full  in  Pisces  or  Aries, 
she  would  aiways  be  full  when  she  came  round  to 
the  same  sign  and  degree  again-     And  as  the  full 
Moon  rises  at  sun- set  (because  when  any  point  of 
the  ecliptic  sets,  the  opposite  point  rises)  she  would 
constantly  rise  within  two  hours  of  sun-set,  on  the 
parallel  of  London,  during  the  week  in  which  she 
was  full.     But  in  the  time  that  the  Moon  goes 
round  the  ecliptic  from  any  conjunction  or  opposi- 
tion, the  Earth  goes  almost  a  sign  forward :    and 
therefore  the  Sun  will  seem  to  go  as  far  forward  in 
that  time,  namely,  27|  degrees ;  so  that  the  Moon 
must  go  27£  degrees  more  than  round,   and  as 
much  farther  as  the  Sun  advances  in  that  interval, 
which  is  2^  degrees,  before  she  can  be  in  conjunc- 
tion with,  or  opposite  to  the  Sun  again.     Hence  it 
is  evident  that  there  can  be  but  one  conjunction  or 
opposition  of  the  Sun  and  Moon  in  a  year  in  any  Her  peri- 
particular  part  of  the  ecliptic.     This  may  be  fami-  odical  and 
liarly  exemplified  by  the  hour  and  minute-hands  oi  revolution 
a  watch,  which  are  never  in  conjunction  or  oppo-  exempiifi- 
sition  in  that  part  of  the  dial-plate  where  they  wereed* 
so  last  before.      And  indeed  if  we  compare  the 
.  twelve  hours  on  the  dial-plate  to  the  twelve  signs  of 
the   ecliptic,    the  hour-hand  to  the  Sun,  and  the 
minute-hand  to  the  Moon,  we  shall  have  a  tolerable 
near  resemblance  in  miniature  to  the  motions  of  our 
great  celestial  luminaries.     The  only  difference  is, 
that  while  the  Sun  goes  once  round  the  ecliptic,  the 
Moon  makes  \^\  conjunctions  with  him:  but,  while 
the  hour-hand  goes  round  the  dial-plate,  the  minute  - 
hand  makes  only  11  conjunctions  with  it;  because  the 
minute-hand  moves  slower  in  respect  to  the  hour- 
Hh 


240  Of  the  'Harvest-Mom. 

hand  than  the  Moon  does  with  regard  to  the  Sun, 

ve^t  and     .    282'  AS  the  M°°n  Can  nCVer  be  ^u11  bllt  wnen  shfe 

Hunter's  ™  opposite  to  the  Sun,  and  the  Sun  is  never  in  Vir- 
Moon.  go  ai.d  Libra,  but  in  our  autumnal  months,  it  is 
p-'iin  that  the  Moon  is  never  full  in  the  opposite  signs, 
Pisces  and  Aries,  but  in  these  two  months.  And 
thercibre  we  can  have  only  two  full  Moons  in  the 
year,  which  rise  so  near  the  time  of  sun-set  for  a 
week  together,  as  above-mentioned.  The  former 
of  these  is  called  the  Harvest  Moon,  and  the  latter 
the  Hunters  Moon. 

Why  the  283.  Here  it  will  probably  be  asked,  why  we  ne- 
regular  ri- ver  observe  this  remarkable  rising  of  the  Moon  but 
is  ne-  in  harvest,  seeing  she  is  in  Pisces  and  Aries  twelve 

times  *n  ^ie  ^car  bes^es  >  an(^  must  then  rise  with 
in  harvest,  as  little  difference  of  time  as  in  harvest?  The  answer 
is  plain  :  for  in  winter  these  signs  rise  at  noon  ;  and 
being  then  only  a  quarter  of  a  circle  distant  from 
the  Sun,  the  Moon  in  them  is  in  her  first  quarter  : 
but  when  the  Sun  is  above  the  horizon,  the  Moon's 
rising  is  neither  regarded  nor  perceived.  In  spring 
these  signs  rise  with  the  Sun,  because  he  is  then  in 
them  ;  and  as  the  Moon  changes  in  them  at  that 
time  of  the  year,  she  is  quite  invisible.  In  sum- 
mer they  rise  about  midnight,  and  the  Sun  being 
then  three  signs,  or  a  quarter  of  a  circle  before 
them,  the  Moon  is  in  them  about  her  third  quarter ; 
and  when  rising  so  late,  and  giving  but  very  lit- 
tle light,  her  rising  passes  unobserved.  And  in 
autumn  these  signs,  being  opposite  to  the  Sun, 
rise  when  he  sets,  with  the  Moon  in  opposition, 
or  at  the  full,  which  makes  her  rising  very  conspi- 
cuous. 

284.  At  the  equator,  the  north  and  south  poles  lie 
in  the  horizon  ;  and  therefore  the  ecliptic  makes  the 
same  angle  southward  with  the  horizon,  when  Aries 
rise  b,  as  it  does  northward  when  Libra  rises.  Conse- 
quently as  the  Moon  at  ail  the  fore-mentioned  patches 
rises  and  sets  nearly  at  equal  angles  with  the  horizon 


Of  the  Harvest-Moon.  24J 

all  the  year  round,  and  about  50  minutes  later  eve- 
ry day  or  night  than  on  the  preceding,  there  can  be 
no  particular  harvest- moon  at  the  equator. 

285.  The  farther  that  any  place  is  from  the  equa- 
tor, if  it  be  not  beyond  the  polar  circle,  the  angle 
gradually  diminishes  which  the  ecliptic  and  horizon 
make  when  Pisces  and  Aries  rise  :  and  therefore 
when  the  Moon  is  in  these  signs  she  rises  with  a 
nearly  proportionable  difference  later  every  day  than 
on  the  former ;  and  is  for  that  reason  the  more  remark- 
able about  the  full,  until  we  come  to  the  polar  cir- 
cles, or  66  degrees  from  the  equator ;  in  which 
latitude  the  ecliptic  and  horizon  become  coincident 
every  day  for  a  moment,  at  the  same  sidereal  hour 
(or  3  minutes  56  seconds  sooner  every  day  than  the 
former),  and  the  very  next  moment  one  half  of  the 
ecliptic,  containing  Capricorn,  Aquarius,  Pisces, 
Aries,  Taurus,  and  Gemini,  rises,  and  the  oppo- 
site half  sets.  Therefore,  while  the  Moon  is  going 
from  the  beginning  of  Capricorn  to  the  beginning 
of  Cancer,  which  is  almost  14  days,  she  rises  at 
the  same  sidereal  hour;  and  in  autumn  just  at  sun-set, 
because  all  the  half  of  the  ecliptic,  in  which  the 
Sun  is  at  that  time,  sets  at  the  same  sidereal  hour, 
and  the  opposite  half  rises ;  that  is,  3  minutes  56 
seconds  of  mean  solar  time,  sooner  every  day  than 
on  the  day  before.  So  while  the  Moon  is  going 
from  Capricorn  to  Cancer,  she  rises  earlier  every 
day  than  on  the  preceding ;  contrary  to  what  she 
does  at  all  places  between  the  polar  circles.  But 
during  the  above  fourteen  days,  tae  Moon  is  24  si- 
dereal hours  later  in  setting  ;  for  the  six  signs  which 
rise  all  at  once  on  the  eastern  side  of  the  horizon  are 
24  hours  in  setting  on  the  western  side  of  it ;  as 
any  one  may  see  by  making  chalk- marks  at  the  be- 
ginning of  Capricorn  and  of  Cancer,  and  then, 
having  elevated  the  pole  66^  degrees,  turn  the  globe 
slowly  round  its  axis,  and  observe  the  rising  and 
setting  of  the  ecliptic.  As  the  beginning  of  Aries 


242  Of  the  Harvest-Moon* 

is  equally  distant  from  the  beginning  of  Cancer  and  ot 
Capricorn,  it  is  in  the  middle  of  that  hall  oi  the 
ecliptic  which  rises  all  at  once.  And  when  the  Sun 
is  at  the  beginning  of  Libra,  he  is  in  the  middle  of 
the  other  half.  Therefore,  when  the  Sun  is  in  Li- 
bra, and  the  Moon  in  Capricorn,  the  Moon  is  a 
quarter  of  a  circle  before  the  Sun ;  opposite  to  him, 
and  consequently  full  in  Aries,  and  a  quarter  of  a 
circle  hehind  him,  when  in  Cancer.  But  when  Li- 
bra rises,  Aries  sets,  and  all  that  half  of  the  eclip- 
tic of  w  hich  Aries  is  the  middle,  and  therefore,  at 
that  time  of  the  year,  the  Moon  rises  at  sun- set 
from  her  first  to  her  third  quarter. 

The  bar.        286.     In  northern  latitudes,    the  autumnal  full 

moons  re-  Moons  are  in  Pisces  and  Aries  >  and  the  vernal  full 

guiaron    Moons  in  Virgo  and  Libra:  in  southern  latitudes, 

ofttheS)deSJust  tne  reverse?   because  the  seasons  are  contrary. 

equator.    But  Virgo  and  Libra  rise  at  as  small  angles  with  the 

horizon  in  southern  latitudes,  as  Pisces  and  Aries 

do  in  the  northern ;  and  therefore  the  harvest- moons 

are  just  as  regular  on  one  side  of  the  equator  as 

on  the  other. 

287.  As  these  signs,  which  rise  with  the  least 
angles,  set  with  the  greatest,  the  vernal  full  Moons 
differ  as  much  in  their  times  of  rising  every  night, 
as  the  autumnal  full  Moons  differ  in  their  times  of 
setting ;  and  set  with  as  little  difference  as  the  au- 
tumnal full  Moons  rise  :   the  one  being  in  all  cases 
the  reverse  of  the  other. 

288.  Hitherto,    for  the  sake  of  plainness,  we 
have  supposed  the  Moon  to  move  in  the  ecliptic, 
from  which  the  Sun  never  deviates.     But  the  orbit 
in  which  the  Moon  really  moves  is  different  from 
the  ecliptic :    one  half  being  elevated   5^  degrees 
above  it,  and  the  other  half  as  much  depressed  be- 
low it.     The  Moon's  orbit  therefore  intersects  the 
ecliptic  in  twTo  points  diametrically  opposite  to  each 
other ;  and  these  intersections  are  called  the  Moon's 
nodes.      So  the  Moon  can  never  be  in  the  ecliptic 


Of  the  Harvest-Moon.  243 

but  when  she  is  in  either  of  her  nodes,  which  is  at  JJlL^ 
least  twice  in  every  course  from  change  to  change, 
and  sometimes  thrice.  For,  as  the  Moon  goes  al- 
most a  whole  sign  more  than  round  her  orbit 
from  change  to  change ;  if  she  passes  by  either 
node  about  the  time  of  change,  she  will  pass  by 
the  other  in  about  fourteen  days  after,  and  come 
round  to  the  former  node  two  days  again  before  the 
next  change.  That  node  from  which  the  Moon  be- 
gins to  ascend  northward,  or  above  the  ecliptic,  in. 
northern  latitudes,  is  called  the  ascending  node; 
and  the  other  the  descending  node;  because  the 
Moon,  when  she  passes  by  it,  descends  below  the 
ecliptic  southward. 

289.  The  Moon's  oblique  motion  with  regard 
to  the  ecliptic  causes  some  difference  in  the  times 
of  her  rising  and  setting  from  what  is  already  men- 
tioned.    For  when  she  is  northward  of  the  eclip- 
tic, she  rises  sooner  and  sets  later  than  if  she  mov- 
ed in  the  ecliptic  ;    and  w?hen  she  is  southward  of 
the  ecliptic,  she  rises  later  and  sets  sooner.     This 
difference  is  variable  even  in  the  same  signs,  be- 
cause the  nodes  shift  backward  about  19-|  degrees 
in  the  ecliptic  every  year  ;  and  so  go  round  it  con- 
trary to  the  order  of  signs  in  18  years  225  days. 

290.  When  the  ascending  node  is  in  Aries,  the 
southern  half  of  the  Moon's  orbit  makes  an  angle 
of  5-J-  degrees  less  yvith  the  horizon  than  the  eclip- 
tic does,  when  Aries  rises  in  northern  latitudes:  for 
which  reason  the  Moon  rises  with  less  difference  of 
time  while  she  is  in  Pisces   and  Aries,  than  she 
would  do  if  she  kept  in  the  ecliptic.      But  in  9 
years  and  112  days  afterward,  the  descending  node 
comes  to  Aries  ;  and  then  the  Moon's  orbit  makes 
an  angle  5~  degrees  greater  with  the  horizon  when 
Aries  rises,  than  the  ecliptic  does  at  that  time; 
which  causes  the  Moon  to  rise  with  greater  differ- 
ence of  time  in  Pisces  3nd  Aries  than  if  she  mov- 
ed in  the  eclipti.c. 


244  Of  the  Harvest-Moon. 

291.  To  be  a  little  more  particular,  when  the 
ascending  node  is  in  Aries,  the  angle  is  only  9|  le- 
grees  on  the  parallel  of  London  when  Aries  rises. 
But  when  the  descending  node  comes  to  Aries,  the 
angle  is  20^  degrees;  this  occasions  as  great  a  dif- 
ference of  the  Moon's  rising  in  the  same  signs  eve- 
ry nine  years,  as  there  would  be  on  two  parallels 
10-f  degrees  from  one  another,  if  the  Moon's  course 
were  in  the  ecliptic.  The  following  table  shews 
how  much  the  obliquity  of  the  Moon's  orbit  affects 
her  rising  and  setting  on  the  parallel  of  London, 
from  the  12th  to  the  18th  day  of  her  age;  suppos- 
ing her  to  be  full  at  the  autumnal  equinox  :  and 
then,  either  in  the  ascending  node,  highest  part  of 
her  orbit,  descending  node,  or  lowest  part  of  her 
orbit.  Jl/ signifies  morning,  A  afternoon  :  and  the 
line  at  the  foot  of  the  table  shews  a  week's  difference 
in  rising  and  setting. 


S  ' 

Full  in  her  Ascend- 
ing Node. 

In  the  highest  pt. 
of  her  Orbit. 

Full  in  her  Descend- 
ing Node. 

In  the  lowest  pt.  of  \ 
her  Orbit.          L 

*J 

Rises  at 

Sots  at 

Rises  at 

Sets  at 

Rises  at 

Sets  at 

Rises  at 

Sets  at     S 

S'S 

H.  M. 

H.  M. 

H.  M. 

H.  M. 

H.  M. 

H.  M. 

H.  M. 

H.  M.     S 

s  -_  

3M  0  £ 

5  A  15 

3M.-0 

4  A  30 

3Afl5 

4  A  32 

3Af40 

5  A  16 

S  13 

5       32 

4     25 

4       50 

4     45 

5       15 

4     20 

6        € 

4     15  V 

Sl4 

5       48 

5     30 

5        15 

6       0 

5       45 

5     40 

6       20 

5    28  S 

S15 

6         5 

7       0 

5       4-2 

7     20 

6       15 

6    56 

6       45 

6    32  S 

S16 

6       20 

8     15 

6         2 

8     35 

6       46 

8       0 

7         8 

7    45  < 

Sir 

6       36 

9     12 

6      26 

9     45 

7       18 

9     15 

7       30 

9     15  S 

Jj  18 

6       54 

10     30 

7         0 

10     40 

8         0 

10     20 

7       52 

10      OS 

S  Diff. 

13       9 

7     10 

2      30 

7      25 

3       28 

6    40 

2      36 

7      0  c 

This  table  was  not  computed,  but  only  estimated 
as  near  as  could  be  done  from  a  common  globe,  on 
which  the  Moon's  orbit  was  delineated  with  a  black- 
lead  pencil.  It  may  at  first  sight  appear  erroneous  ; 
since  as  we  have  supposed  the  Moon  to  be  full  in 
either  node  at  the  autumnal  equinox,  ought  by  the 


Of  the  Harvest-Moon.  245 

table  to  rise  just  at  six  o'clock,  or  at  sun-set,  on  the 
ISthday  of  her  age;  being  in  the  ecliptic  at  that  time. 
But  it  must  be  considered,  that  the  Moon  is  only 
14»  days  old  when  she  is  full ;  and  therefore  in  both 
cases  she  is  a  little  past  the  node  on  the  15th  day, 
being  above  it  at  one  time,  and  below  it  at  the  other. 

292.  As  there  is  a  complete  revolution  of  the  The  peri- 
nodes  in  18f  years,  there  must  be  a  regular  period  j 
of  all  the  varieties  which  can  happen  in  the  rising  moon, 
and  setting  of  the  Moon  during  that  time.  But  this 
shifting  of  the  nodes  never  affects  the  Moon's  rising 
so  much,  even  in  her  quickest  descending  latitude, 
as  not  to  allow  us  still  the  benefit  of  her  rising  nearer 
the  time  of  sun- set  for  a  few  day  together  about  the 
full  in  harvest,  than  when  she  is  full  at  any  other 
time  of  the  year.  The  following  table  shews  in  what 
years  the  harvest- moons  are  least  beneficial  as  to  the 
times  of  their  rising,  and  in  what  years  most,  from 
1751  to  1861.  The  column  of  years  under  the  let- 
ter L  are  those  in  which  the  harvest- moons  are  least 
of  all  beneficial,  because  they  fall  about  the  descend- 
ing node:  and  those  under  J/are  the  most  of  all 
beneficial,  because  they  fall  about  the  ascending 
node.  In  all  the  columns  from  N  to  S  the  harvest- 
moons  descend  gradually  in  the  lunar  orbit,  and  rise 
to  less  heights  above  the  horizon.  From  S  to  A" 
they  ascend  in  the  same  proportion,  and  rise  to  great- 
er heights  above  the  horizon.  In  both  the  columns 
under  £,  the  harvest- moons  are  in  the  lowest  part 
of  the  Moon's  orbit,  that  is,  farthest  south  of  the 
ecliptic,  and  therefore  stay  shortest  of  all  above  the 
horizon :  in  the  columns  under  A",  just  the  reverse. 
And  in  both  cases,  their  risings,  though  not  at  the 
same  times,  are  nearly  the  same  with  regard  to  dif- 
ference of  time,  as  if  the  Moon's  orbit  were  coinci- 
dent with  the  ecliptic. 


246 


Of  the  Harvest-Moon. 


Years  in  which  the  Harvest- Moons  are  least  bentjicial. 

N  L  S 

1751  1752  1753  1754  1755  1756  1757  1758  1759 
1770  1771  1772  1773  1774  1775  1776  17.77  1778 
1788  1789  1790  1791  1792  1793  1794  1795  1796   1797 
1807  1808  1809  1810  1811  1812  1813  1814  1815 
1826  1827  1828  1829  1830  1831  1832  1833  1834   t 
1844  1845  1846  1847  1848  1849  1850  1851  1852 

Years  in  which  they  are  most  beneficial. 
S  M  N 

1760  1761  1762  1763  1764  1765  1766  176?  1768   1769 
1779  1780  1781  1782  1783  1784  1785  1786  1787 
1798  1799  1800  1801  1802  1803  1804  1805  18u6 
1816  1817  1818  1819  1820  1821  1822  1823  1824   1825 
1835  1836  1837  1838  1839  1840  1841  1842  1843 
1853  1854  1855  1856  1857  1858  1859  1860  1861 


The  long- 
continu- 
ance of 
moon- 
light at 
the  poles. 


293.  At  the  polar  circles,  when  the  Sun  touches 
the  summer-tropic,  he  continues  24  hours  above 
the  horizon;  and  24  hours  below  it  when  he  touches 
the  winter-tropic.     For  the  same  reason  the  full 
Moon  neither  rises  in  summer,  nor  sets  in  winter, 
considering  her  as  moving  in  the  ecliptic.    For  the 
winter  full  Moon  being  as  high  in  the  ecliptic  as  the 
summer  Sun,  must  therefore  continue  as  long  above 
the  horizon  ;  and  the  summer  full  Moon  being  as 
low  in  the  ecliptic  as  the  winter  Sun,  can  no  more 
rise  than  he  does.     But  these  are  only  the  two  full 
Moons  which  happen  about  the  tropics,  for  all  the 
others  rise  and  set.    In  summer  the  full  Moons  are 
low,  and  their  stay  is  short  above  the  horizon,  when 
the  nights  are  short,  and  we  have  least  occasion  for 
moon-light :  in  winter  they  go  high,  and  stay  long 
above  the  horizon,  when  the  nights  are  long,  and  we 
want  the  greatest  quantity  of  moon- light. 

294.  At  the  poles,  one  half  of  the  ecliptic  never 
sets,  and  the  other  half  never  rises :  and  therefore, 
as  the  Sun  is  always  half  a  year  in  describing  one 
half  of  the  ecliptic,  and  as  long  in  going  through 


The  long  Duration  of  Moon-  light  at  the  Poles.  24! 

the  other  half,  it  is  natural  to  imagine  that  the  Sun 
continues  half  a  year  together  above  the  horizon  of 
each  pole  in  its  turn,  and  as  long  below  it ;  rising  to 
one  pole  when  he  sets  to  the  other.  This  would  be 
exactly  the  case  if  there  were  no  refraction  ;  but  by 
the  atmosphere's  refracting  the  Sun's  rays,  he  be- 
comes visible  some  days  sooner,  §  183,  and  contin- 
ues some  days  longer  in  sight  than  he  would  other- 
wise do :  so  that  he  appears  above  the  horizon  of  ei- 
ther pole  before  he  has  got  below  the  horizon  of  the 
other.  And,  as  he  never  goes  more  than  23-  de- 
grees below  the  horizon  of  the  poles,  they  have 
very  little  dark  night ;  it  being  twilight  there  as  well 
as  at  all  other  places,  till  the  Sun  is  18  degrees 
below  the  horizon,  §  177.  The  full  Moon  being  al- 
ways opposite  to  the  Sun,  can  never  be  seen  while 
the  Sun  is  above  the  horizon,  except  when  the  Moon 
fulls  in  the  northern  half  of  her  orbit ;  for  whenever 
any  point  of  the  ecliptic  rises,  the  opposite  point  sets. 
Therefore,  as  the  Sun  is  above  the  horizon  of  the 
north  pole  from  the  20th  of  March  till  the  23d  of 
September,  it  is  plain  that  the  Moon,  when  full,  be- 
ing opposite  to  the  Sun,  must  be  below  the  horizon 
during  that  half  of  the  year.  But  when  the  Sun  is  in 
the  southern  half  of  the  ecliptic,  he  never  rises  to  the 
north  pole,  during  which  half  of  the  year,  every  full 
Moon  happens  in  some  part  of  the  northern  half  of 
the  ecliptic,  which  never  sets.  Consequently,  as 
the  polar  inhabitants  never  see  the  full  Moon  in  sum- 
mer, they  have  her  always  in  the  winter,  before, 
at,  and  after  the  full,  shining  for  14  of  our  clays 
and  nights.  And  when  the  Sun  is  at  his  greatest 
depression  below  the  horizon,  being  then  in  Capri- 
corn, the  Moon  is  at  her  first  quarter  in  Aries,  full 
in  Cancer,  and  at  her  third  quarter  in  Libra.  And 
as  the  beginning  of  Aries  is  the  rising  point  of  the 
ecliptic,  Cancer  the  highest,  and  Libra  the  setting 
point,  the  Moon  rises  at  her  first  quarter  in  Aries, 
is  most  elevated  above  the  horizon,  and  full  in  Can- 
cer,  and  sets  at  the  beginning  of  Libra  in  her  third 
I  i 


248          The  long  Duration  of  Moon-light  at  the  Poles. 


PLATE 
VIII. 


quarter,  having  continued  visible  for  14  diurnal  ro- 
tations of  the  Earth.  Thus  the  poles  are  supplied 
one  half  of  the  winter-time  with  constant  moon,  light 
in  the  Sun's  absence ;  and  only  lose  sight  of  the 
Moon  from  her  third  to  her  first  quarter,  while  she 
gives  but  very  little  light,  and  could  be  but  of  lit- 
v.  tie,  and  sometimes  of  no  service  to  them.  A  bare 
view  of  the  figure  will  make  this  plain  :  in  which  let 
8  be  the  Sun,  e  the  Earth  in  summer,  when  its 
jiorth  pole  n  inclines  toward  the  Sun,  and  E  the 
Earth  in  winter,  when  its  north  pole  declines  from 
him.  SEN  and  NIPS  is  the  horizon  of  the  north 
pole,  which  is  coincident  with  the  equator  ;  and,  in 
both  these  positions  of  the  Earth,  <Y>  &  —  V?  is  the 
Moon's  orbit,  in  which  she  goes  round  the  Earth, 
according  to  the  order  of  the  letters  abed,  ABCD. 
When  the  Moon  is  at  «,  she  is  in  her  third  quarter 
to  the  Earth  at  e,  and  just  rising  to  the  north  pole  n; 
at  b  she  changes,  and  is  at  the  greatest  height  above 
the  horizon,  as  the  Sun  likewise  is;  at  c  she  is  in 
her  first  quarter,  setting  below  the  horizon  ;  and  is 
lowest  of  all  under  it  at  c/,  when  opposite  to  the 
Sun,  and  her  enlightened  side  toward  the  Earth. 
But  then  she  is  full  in  view  to  the  south  pole  p ; 
which  is  as  much  turned  from  the  Sun  as  the  north 
pole  inclines  toward  him.  Thus  in  our  summer, 
the  Moon  is  above  the  horizon  of  the  north  pole, 
while  she  describes  the  northern  half  of  the  ecliptic 
T  25  =3= ,  or  from  her  third  quarter  to  her  first ;  and 
below  the  horizon  during  her  progress  through  the 
southern  half  =2=  yj  v  ;  highest  at  the  change,  most 
depressed  at  the  full.  But  in  winter,  when  the 
Earth  is  at  E,  and  its  north  pole  declines  from  the 
Sun,  the  new  Moon  at  D  is  at  her  greatest  depres- 
sion below  the  horizon  A/FiS1,  and  the  lull  Moon  at 
B  at  her  greatest  height  above  it ;  rising  at  her  first 
quarter  A,  and  keeping  above  the  horizon  till  she 
comes  to  her  third  quarter  C.  At  a  mean  state  she 
is  123|-  degrees  above  the  horizon  at  B  and  b,  and  as 
much  below  it  at  D  and  d,  equal  to  the  inclination 


Of  the  Tides.  249 

of  the  Earth's  axis  F.  S  &  or  S  v$  is,  as  it  were, 
a  ray  of  light  proceeding  from  the  Sun  to  the  Earth ; 
and  shews  that  when  the  Earth  is  at  e,  the  Sun  is 
above  the  horizon,  vertical  to  the  tropic  of  Cancer; 
and  when  the  Earth  is  at  E,  he  is  below  the  horizon, 
vertical  to  the  tropic  of  Capricorn. 

CHAP.  XVII. 

Of  the  Ebbing  and  Flowing  of  the  Sea. 

HE  cause  of  the  tides  was  discovered  by 
KEPLER,  who,  in  his  /;/ 1 reduction  to  the 
Physics  of  the  Heavens,  thus  explains  it  :  "  The  The  cause 
orb  of  the  attracting  power,  which  is  in  the  Moon,  °.f1the1. 

i     i         r  A       frxLut  i  j  '  tides  dis- 

is  extended  as  far  as  the  Earth ;  and  draws  the  wa-  coveredby 

ters  under  the  torrid  zone,  acting  upon  places  where  KEPLER. 

it  is  vertical,  insensibly  on  confined  seas  and  bays, 

but  sensibly  on  the  ocean,  whose  beds  are  large, 

and  the   waters  have  the  liberty  of  reciprocation  ; 

that  is,  of  rising  and  falling."      And  in  the  70th 

page  of  his  Lunar  Astronomy — "  But  the  cause  of 

the  tides  of  the  sea  appears  to  be  the  bodies  of  the 

Sun  and  Moon  drawing  the  waters  of  the  sea." — 

This  hint  being  given,    the  immortal   Sir   ISAAC  Their  the- 

NEWTON  improved  it,  and  wrote  so  amply  on  the01"??115?" 

.  .  c.    ,      r.<        .          ved  by  Sir 

subject,  as  to  make  the  theory  or  the  tides  in  a  ISAAC 
manner  quite  his  own;  by  discovering  the  cause  ofNEWTON- 
their  rising  on  the  side  of  the  Earth  opposite  to  the 
Moon.     For  KEPLER  believed,  that  the  presence 
of  the  Moon  occasioned  an  impulse  which  caused 
another  in  her  absence. 

296.     It  has  been  already  shewn,  $  106,  that  Explain- 
the  power  of  gravity  diminishes  as  the   square  oft?  OI?  th-e 

,       \.  .     P      ,4  y  „  Newtoni- 

the  distance  increases  ;    and  therefore  the  waters  at  an  princi- 
Z,  on  the  side  of  the  Earth  ABCDEFGH  nextP1^- 
the  Moon  M,   are  more  attracted  than  the  central  PLATR 
parts  of  the  Earth  0  by  the  Moon,  and  the  central      IX* 
parts  are  more  attracted  by  her  than  the  waters  on  Tig.  I. 
the  opposite    side  of  the  Earth  at  n :    and  there- 


250  Of  the  Tides. 

PLATE  fore  the  distance  between  the  Earth's  centre  and 
the  waters  on  its  surface  under  and  opposite  to  the 
Moon  will  be  increased.  For,  let  there  be  three 
bodies  at  //,  0,  and/).-  if  they  be  all  equally  at- 
tracted by  the  body  M,  they  will  all  move  equally 
fast  toward  it,  their  mutual  distances  from  each 
other  continuing  the  same.  If  the  attraction  of  M 
be  unequal,  then  that  body  which  is  most  strongly 
attracted  will  move  fastest,  and  this  will  increase  its 
distance  from  the  other  body.  Therefore,  by  the 
law  of  gravitation,  M \vi\\  attract  //more  strongly 
than  it  does  0,  by  which  the  distance  between  H 
and  O  will  be  increased :  and  a  spectator  on  O  will 
perceive  H  rising  higher  toward  Z.  In  like 
manner,  O  being  more  strongly  attracted  than 
/),  it  will  move  farther  toward  M  than  D  does  : 
consequently,  the  distance  between  0  and  D  will 
be  increased  ;  and  a  spectator  on  O,  not  perceiving 
his  own  motion,  will  see  D  receding  farther  from 
him  toward  n  :  all  effects  and  appearances  being  the 
same,  whether  D  recedes  from  O9  or  0  from  /). 
297.  Suppose  now  there  is  a  number  of  bodies, 
as  A,  B,  C,  /),  E,  F,  G,  H,  placed  round  O,  so 
as  to  form  a  flexible  or  fluid  ring :  then,  as  the 
whole  is  attracted  towards  M,  the  parts  at  H  and 
D  will  have  their  distance  from  O  increased ;  while 
the  parts  at  B  and  F,  being  nearly  at  the  same  dis- 
tance from  Mas  O  is,  these  parts  will  not  recede 
from  one  another ;  but  rather,  by  the  oblique  attrac- 
tion oi'My  they  will  approach  nearer  to  O.  Hence, 
the  fluid  ring  will  form  itself  into  an  ellipse  Z I  B 
L  n  K  F  N  Z,  whose  longer  axis  n  0  Z  produced 
will  pass  through  M,  and  its  shorter  axis  B  0  F 
will  terminate  in  B  and  F.  Let  the  ring  be  filled 
with  fluid  particles,  so  as  to  form  a  sphere  round  0; 
then,  as  the  whole  moves  toward  M,  the  fluid  sphere 
being  lengthened  at  Z  and  n>  will  assume  an  ob- 
long or  oval  form.  If  M  be  the  Moon,  O  the 
Earth's  centre,  ABCDEFGH  the  sea  covering  the 


Of  the  Tides.  251 

Earth's  surface,  it  is  evident,  by  the  above  reason-  } 
ing,  that  while  the  Earth  by  its  gravity  falls  toward 
the  Moon,  the  water  directly  below  her  at  B  will 
swell  and  rise  gradually  toward  her  :  also  the  water 
at  D  will  recede  from  the  centre  (strictly  speaking, 
the  centre  recedes  from  D),  and  rise  on  the  opposite 
side  of  the  Earth :  while  the  water  at  B  and  JP  is 
depressed,  and  falls  below  the  former  level.  Hence, 
as  the  Earth  turns  round  its  axis  from  the  Moon  to 
the  Moon  again,  in  24|  hours,  there  will  be  two 
tides  of  flood  and  two  of  ebb  in  that  time,  as  we 
find  by  experience. 

298.  As  this  explanation  of  the  ebbing  and  flow- 
ing of  the  sea,  is  deduced  from  the  Earth's  con- 
stantly falling  toward  the  Moon  by  the  power  of  gra- 
vity, some  may  find  a  difficulty  in  Conceiving  how 
this  is  possible,  when  the  Moon  is  full,  or  in  oppo- 
sition to  the  Sun ;  since  the  Earth  revolves  about 
the  Sun,  and  must  continually  fall  toward  it,  and 
therefore  cannot  fall  contrary  ways  at  the  same  time : 
or,  if  the  Earth  be  constantly  falling  toward  the  Moon, 
they  must  come  together  at  last.  To  remove  this 
difficulty,  let  it  be  considered,  that  it  is  not  the  cen- 
tre of  the  Earth  that  describes  the  annual  orbit  round 
the  Sun,  but  the*  common  centre  of  gravity  of  the 
Earth  and  Moon  together :  and  that  while  the  Earth 
is  moving  round  the 'Sun,  it  also  describes  a  circle 
round  that  centre  of  gravity ;  going  as  many  times 
round  it  in  one  revolution  about  the  Sun  as  there 
are  lunations  or  courses  of  the  Moon  round  the 
Earth  in  a  year :  and  therefore,  the  Earth  is  con- 
stantly falling  toward  the  Moon  from  a  tangent  to 
the  circle  it  describes  round  the  said  common  cen- 
tre of  gravity.  Let  Mbe  the  Moon,  T  W part  of 

*  This  centre  is  as  much  nearer  the  Earth's  centre  than  the 
Moon's,  as  the  Earth  is  heavier,  or  contains  a  greater  quantity  of 
matter  than  the  Moon,  namely,  about  40  times.  It^both  bodies 
were  suspended  on  it,  they  would  hang  in  equilibria.  So  that  divid- 
ing 240,000  miles,  the  Moon's  distance  from  the  Earth's  centre,  by 
40,  the  excess  of  the  Earth's  weight  above  the  Moon's,  the  quotient 
will  be  6000  miles,  which  is  the  distance  of  the  common  centre  of 
gravity  of  the  Earth  and  Moon  from  the  Earth's  centre. 


252  Of  the  Tides. 


PLATE  the  Moon's  orbit,  and  C  the  centre  of  gravity  of 
the  Earth  ;ind  Moon;  while  the  Moon  goes  round 
Fig.  ii.  her  orbit,  the  centre  of  the  Earth  describes  the  cir- 
cle dg  around  C,  to  which  circle ga  k  is  a  tangent: 
and  therefore,  when  the  Moon  has  gone  from  M  to 
a  little  past  W,  the  Earth  has  moved  from  g  to  e; 
and  in  that  time  has  fallen  toward  the  Moon,  from 
the  tangent  at  a  to  c ;  and  so  on,  round  the  whole 
circle. 

299.  The  Sun's  influence  in  raising  the  tides  is 
but  small  in  comparison  of  the  Moon's ;  for  though 
the  Earth's  diameter  bears  a  considerable  propor- 
tion to  its  distance  from  the  Moon,  it  is  next  to  no- 
thing when  compared  to  its  distance  from  the  Sun. 
And  therefore,  the  difference  of  the  Sun's  attrac- 
tion on  the  sidfts  of  the  Earth  under  and  opposite 
to  him,  is  much  less  than  the  difference  of  the 
Moon's  attraction  on  the  sides  of  the  Earth  under 
and  opposite  to  her  :  and  therefore  the  Moon  must 
raise  the  tides  much  higher  than  they  can  be  raised 
by  the  Sun. 

why  the  300.  On  this  theory,  so  far  as  we  have  explained 
n<rtehiST-  fr»  the  tlc^es  ought  to  be  highest  directly  under  and 
est  when  opposite  to  the  Moon ;  that  is,  when  the  Moon  is 

iiTo^thT  ^ue  nort1tt  and  soutn-   But  we  find,  tnat  in  °pen 

merman,  seas,  where  the  water  flow  sfreely,  the  Moon  M  is 
generally  past  the  north  and  south  meridian,  as  atp, 

Fig.  I.  when  it  is  high  water  at  Z  and  at  n.  The  reason 
is  obvious;  for  though  the  Moon's  attraction  were 
to  cease  altogether  when  she  was  past  the  meridian, 
yet  the  motion  of  ascent  communicated  to  the  wa- 
ter before  that  time  would  make  it  continue  to  rise 
for  some  time  after ;  much  more  must  it  do  so  when 
the  attraction  is  only  diminished:  as  a  little  impulse 
given  to  a  moving  ball  will  cause  it  still  to  move  far- 
ther than  otherwise  it  could  have  done.  And  as  ex- 
perience shews,  that  the  day  is  hotter  about  three  in 


Of  the  Tides.  253 

the  afternooiTthan  when  the  Sun  is  on  the  meridian,    PLATE 
because  of  the  increase  made  to  the  heat  already      IX< 
imparted. 

301.  The  tides  answer  not  always  to  the  sameNoral- 
distance  of  the  Moon  from  the  meridian  at  the  same  Twer  to" 
places ;  but  are  variously  affected  by  the  action  of her  bein£ 
the  Sun,  which  brings  them  on  sooner  when  the  ^^dis- 
Moon  is  in  her  first  and  third  quarters,  and  keepstancefi-om 
them  back  later  when  she  is  in  her  second  and  fourth : 1U 
because,  in  the  former  case,  the  tide  raised  by  the 

Sun  alone  would  be  earlier  than  the  tide  raised  by 
the  Moon ;  and  in  the  latter  case  later. 

302.  The  Moon  goes  round  the  Earth  in  an  ellip- 
tic orbit,  and  therefore,  in  every  lunar  month,  she 
approaches  nearer  to  the  Earth  than  her  mean  dis- 
tance, and  recedes  farther  from  it .    When  she  is  near-  Spring 
est,  she  attracts  strongest,  and  so  raises  the  tides 
most;  the  contrary  happens  when  she  is  farthest,  be- 
cause of  her  weaker  attraction.    When  both  lumina- 
ries are  in  the  equator,  and  the  Moon  in  perigeo,  or 

at  her  least  distance  from  the  Earth,  she  raises  the 
tides  highest  of  all,  especially  at  her  conjunction  and 
opposition  ;  both  because  the  equatorial  parts  have 
the  greatest  centrifugal  force  from  their  describing 
the  largest  circle,  and  from  the  concurring  actions 
of  the  Sun  and  Moon.  At  the  change,  the  attractive 
forces  of  the  Sun  and  Moon  being  united,  they  di- 
minish the  gravity  of  the  waters  under  the  Moon, 
and  their  gravity  on  the  opposite  side  is  diminished 
by  means  of  a  greater  centrifugal  force.  At  the  full,  Fi 
while  the  Moon  raises  the  tide  under  and  opposite 
to  her,  the  Sun,  acting  in  the  same  line,  raises  the 
tide  under  and  opposite  to  him ;  whence  their  con- 
joint effect  is  the  same  as  at  the  change;  and  in  both 
cases,  occasion  what  we  call  the  spring  tides.  But 
at  the  quarters  the  Sun's  action  on  the  waters  at  O 
and  //diminishes  the  effect  of  the  Moon's  action  on 
the  waters  at  Z  and  N;  so  that  they  rise  a  little  un- 
der and  opposite  to  the  Sun  at  0  and  H,  and  fall  as 


254  Of  the  Tides. 

much  under  and  opposite  to  the  Moon  at  Z  and  N; 
making  what  we  call  the  neap  tides,  because  the  Sun 
and  Moon  then  act  cross-  wise  to  each  other.  But, 
strictly  speaking,  these  tides  happen  not  till  some 
time  after  ;  because  in  this,  as  in  other  cases,  \  300, 
the  actions  do  not  produce  the  greastet  effect  when 
they  are  at  the  strongest,  but  some  time  afterward. 
Not  great-  303.  The  Sun  being  nearer  the  Earth  in  winter 
l^an  m  summer>  $  ^05,  *s  °f  course  nearer  to  it  in 


equnox 

es,  and      February  and  October,  than  in  March  and  Septem- 


ber  ;  and  therefore  the  greatest  tides  happen  not  till 

some  time  after  the  autumnal  equinox,  and  return  a 

little  before  the  vernal. 
The  tides  The  sea  being  thus  put  in  motion,  would  conti- 
™uli"otnue  to  ebb  and  flow  for  several  times,  even  though 
ateiycea"ge  the  Sun  and  Moon  were  annihilated,  or  their  influ- 
upon  the  eiice  should  cease  :  as  if  a  bason  of  water  were  agi- 
tionof  thetate<^'  tne  water  would  continue  to  move  for  some 
Sun  and  time  after  the  bason  was  left  to  stand  still.  Or  like 
Moon.  a  penciulum,  which,  having  been  put  in  motion  by 

the  hand,  continues  to  make  several  vibrations  with- 

out any  hew  impulse. 

The  lunar     304.  When  the  Moon  is  in  the  equator,  the  tides 

The  Tides  are  ecllia%  high  m  ^otn  Parts  °^  tne  ^unar  day,  or 
rise3  to1  estime  of  the  Moon's  revolving  from  the  meridian  to 
unequal  the  meridian  again,  which  is  24  hours  50  minutes. 
the&samem^ut  as  tne  Moon  declines  from  the  equator  toward 
day,  and  either  pole,  the  tides  are  alternately  higher  and  lower 
at  places  having  north  or  south  latitude.  For  one  of 
the  highest  elevations,  which  is  that  under  the  Moon, 
follows  her  toward  the  pole  to  which  she  is  nearest,  and 
the  other  declines  toward  the  opposite  pole;  each  ele- 
vation describing  parallels  as  far  distant  from  the  equa- 
tor, on  opposite  sides,  as  the  Moon  declines  from  it 
to  either  side  ;  and  consequently,  the  parallels  de- 
scribed by  these  elevations  of  the  water  are  twice  as 
many  degrees  from  one  another,  as  the  Moon  is  from 
the  equator;  increasing  their  distance  as  the  Moon 


Of  the  Ticks.  255 


increases  her  declination,   till  it  be  at  the  greatest, 
when  the  said  parallels  are,  at  a  mean  state,  47  de- 
grees from  one  another  :  and  on  that  day,  the  tides 
are  most  unequal  in  their  heights.  As  the  Moon  re- 
turns toward  the  equator,  the  parallels  described  by 
the  opposite  elevations  approach  toward  each  other, 
until  the  Moon  comes  to  the  equator,  and  then  they 
coincide.   As  the  Moon  declines  towards  the  oppo- 
site pole,  at  equal  distances,  each  elevation  describes 
the  same  parallel  in  the  other  part  of  the  lunar  day, 
which  its  opposite  elevation  described   before.— 
While  the  Moon  has  north  declination,  the  greatest 
tides  in  the  northern  hemisphere  are  when  she  is 
above  the  horizon,  and  the  reverse  while  her  decli- 
nation is  south.   Let  N  E  S  Q  be  the  Earth,  JV  C  S  Fiff.  Hi* 
its  axis,  E  Q  the  equator,  T  25  the  tropic  of  Can-  IV*  ^- 
cer,  t  V5  the  tropic  of  Capricorn,  a  b  the  arctic  cir- 
cle, edthe  antarctic,  JVthe  north  pole,   S  the  south 
pole,  Jl/the  Moon,  F  and  G  the  two  eminences  of 
water,  whose  lowest  parts  are  at  #and  d  (Fig.  III.) 
at  AT  and  S  (Fig.  IV.)  and  at  b  and  c  (Fig.  V.)  al- 
ways 90  degrees  from  the  highest.    Now  when  the 
Moon  is  in  her  greatest  north  declination  at  j\f,  the 
highest  elevation  G  under  her,   is  .  on  the  tropic  of 
Cancer  T  25,  and  the  opposite  elevation  F  on  the  Fig,  lit, 
tropic  of  Capricorn,  t  vj  ;  and  these  two  elevations 
describe  the  tropics  by  the  Earth's  diurnal  rotation. 
All  places  in  the  northern  hemisphere  E  N  Q 
have  the  highest  tides  when  they  come  into  the  po- 
sition b  gs  Q,  under  the  Moon;  and  the  lowest  tides 
when  the  Earth's  diurnal  rotation  carries  them  into 
the  position  a  T  E,  on  the  side  opposite   to  the 
Moon  ;  the  reverse  happens  at  the  same  time  in  the 
southern  hemisphere  E  S  Q,  as  is  evident  to  sight. 
The  axis  of  the  tides  a  C  d  has  now  its  poles  a  and 
d  (being  always  90  degrees  from  the  highest  eleva- 
tions) in  the  arctic  and  antarctic  circles  ;  and  there- 
fore it  is  plain,  that  at  these  circles  there  is  but  one  tide 

Kk 


Of  the  Tides. 


PLATE 
IX. 


of  flood  and  one  of  ebb,  in  the  lunar  day.  For,  when  the 
point  a  revolves  half  round  to  />,  in  12  lunar  hours  it 
Fi£- 1V-  has  a  tide  of  flood;  but  when  itcomes  tothe  same  point 
a  again  in  12  hours  more,  it  has  the  lowest  ebb.  In 
seven  days  afterward,  the  Moon  M  comes  to  the 
equinoctial  circle,  and  is  over  the  equator  E  Q,  when 
both  elevations  describe  the  equator ;  and  in  both 
hemispheres,  at  equal  distances  from  the  equator, 
the  tides  are  equally  high  in  both  parts  of  the  lunar 
day.  The  whole  phenomena  being  reversed,  when 
Fig.  v.  the  Moon  has  south  declination,  to  what  they  W7ere 
when  her  declination  was  north,  require  no  farther 
description. 

305.  In  the  three  last-mentioned  figures,  the  earth 
is  orthographically  projected  on  the  plane  of  the  me- 
ridian ;  but  in  order  to  describe  a  particular  pheno- 
menon, we  now  project  it  on  the  plane  of  the  ecliptic, 
rig.  vi.    Let  HZO  A'be  the  earth  and  sea,  FE  D  the  equa- 
tor,  T  the  tropic  of  Cancer,  C  the  arctic  circle,  P 
the  north  pole,  and  the  curves  1,  2,  3,  &c.  24  meri- 
dians, or  hour-circles,  intersecting  each  other  in  the 
When       poles;  AGMis  the  Moon's  orbit,   S  the  Sun,  M 
are  equal-  tne  Moon,  Zthe  water  elevated  under  the  Moon,  and 
ly  high  in  JVthe  opposite  equal  elevation.    As  the  lowest  parts 

da6  "the6  of  tlie  water  are  ahva}TS  90  degrees  from  the  highest, 
arrive  aT  when  the  Moon  is  in  either  of  the  tropics  (as  at  M) 
unequal  ^  elevation  Z  is  oil  the  tropic  of  Capricorn,  and  the 

intervals  .         ,  ,  •         r  /-< 

of  time ;  opposite  elevation  N  on  the  tropic  of  Lancer  ;  the 
andsofce  low- water  circle  HC  0  touches  the  polar  circles  at 
C,  and  the  high- water  circle  E  TP  6  goes  over 
the  poles  at  P,  and  divides  every  parallel  of  latitude 
into  two  equal  segments.  In  this  case,  the  tides  upon 
every  parallel  are  alternately  higher  and  lower;  but 
they'  return  in  equal  times :  the  point  T,  for  example, 
'  on  the  tropic  of  Cancer  (where  the  depth  of  the  tide 
is  represented  by  the  breaclth  of  the  dark  shade)  has 
a  shallower  tide  of  flood  at  T,  than  when  it  revolves 
half  round  from  thence  to  6,  according  to  the  order 


Of  the  Tufa.  257 

of  the  numeral  figures ;  but  it  revolves  as  soon  from 
6  to  T^as  it  did  from  Tto  6.  When  the  Moon  is 
in  the  equinoctial,  the  elevations  Z  and  A*  are  trans- 
ferred  to  the  equator  at  0  and  //,  and  the  high  and 
low- water  circles  are  got  into  each  other's  former 
places;  in  which  case  the  tides  return  in  unequal 
times,  but  arc  equally  high  ii*  parts  of  the  lunar  day : 
for  a  place  at  1  (under  D]  revolving  as  formerly,  goes 
sooner  from  1  to  11  (under  F)  than  from  11  to  1, 
because  the  parallel  it  describes  is  cut  into  unequal 
segments  by  the  high- water  circle  IICO  :  but  the 
points  1  and  11  being  equidistant  from  the  pole  of 
the  tides  at  C,  which  is  directly  under  the  pole  of 
the  Moon's  orbit  MGA,  the  elevations  are  equally 
high  in  both  parts  of  the  day. 

306.  And  thus  it  appears,  that  as  the  tides  are  go- 
verned by  the  Moon,  they  must  turn  on  the  axis  of 
the  Moon's  orbit,  which  is  inclined  23~  degrees  to 
the  Earth's  axis  at  a  mean  state :  and  therefore  the 
poles  of  the  tides  must  be  so  many  degrees  from  the 
poles  of  the  Earth,  or  in  opposite  points  of  the  polar 
circles,  going  round  these  circles  in  every  lunar  day. 
It  is  true,  that  according  to  Fig.  IV.  when  the  Moon 
is  vertical  to  the  Equator  -ECQ,  the  poles  of  the 
tides  seem  to  fall- in  with  the  poles  of  the  world  A" 
and  S;  but  when  we  consider  that  FGH  is  under 
the  Moon's  orbit,  it  will  appear,  that  when  the  Moon 
is  over  //,  in  the  tropic  of  Capricorn,  the  north  pole 
of  the  tides  (which  can  be  no  more  than  90  degrees 
from  under  the  Moon)  must  be  at  C  in  the  arctic 
circle,  not  at  P,  the  north  pole  of  the  Earth  ;  and 
as  the  Moon  ascends  from  Hto  G  in  her  orbit,  the 
north  pole  of  the  tides  must  shift  from  c  to  a  in  the 
arctic  circle,  and  the  south  pole  as  much  in  the  an- 
tarctic. 

It  is  not  to  be  doubted,  but  that  the  Earth's  quick 
rotation  brings  the  poles  of  the  tides  nearer  to  the 


258  Of  the  Tides. 

poles  of  the  world,  than  they  would  be  if  the  Earth 
were  at  rest,  and  the  Moon  revolved  about  it  only 
once  a  month;  for  otherwise  the  tides  would  be  more 
unequal  in  their  heights,  and  times  of  their  returns, 
than  we  find  they  are.  But  how  near  the  Earth's 
rotation  may  bring  the  poles  of  its  axis  and  those  of 
the  tides  together,  or  how  far  the  preceding  tides 
may  affect  those  which  follow,  so  as  to  make  them 
keep  up  nearly  to  the  same  heights,  and  times  of 
ebbing  and  flowing,  is  a  problem  more  fit  to  be 
solved  by  observation  than  by  theory. 


Those  who  have  opportunity  to  makt  obser- 
vations,  and  choose  to  satisfy  themselves  whether 
may  ex-  the  tides  are  really  affected  in  the  above  manner  by 
latest  tne  different  positions  of  the  Moon,  especially  as  to 
and  least  the  unequal  times  of  their  returns,  may  take  this  ge- 
neral rule  for  knowing  when  they  ought  to  be  so  af- 
fected. When  the  Earth's  axis  inclines  to  the  Moon, 
the  northern  tides,  if  not  retarded  in  their  passage 
through  shoals  and  channels,  nor  affected  by  the 
winds,  ought  to  be  greatest  when  the  Moon  is  above 
the  horizon,  least  when  she  is  below  it  ;  and  quite 
the  reverse  when  the  Earth's  axis  declines  from  her  : 
but  in  both  cases,  at  equal  intervals  of  time.  When 
the  Earth's  axis  inclines  sidewise  to  the  Moon,  both 
tides  are  equally  high,  but  they  happen  at  unequal 
intervals  of  time.  In  every  lunation,  the  Earth's 
axis  inclines  once  to  the  Moon,  once  from  her,  and 
twice  sidewise  to  her,  as  it  does  to  the  Sun  every 
year  :  because  the  Moon  goes  round  the  ecliptic  eve- 
ry month,  and  the  Sun  but  once  in  a  year.  In  sum- 
mer, the  Earth's  axis  inclines  toward  the  Moon  when 
new  ;  and  therefore  the  day-tides  in  the  north  ought 
to  be  highest,  and  night-  tides  lowest,  about  the 
change  :  at  the  full  the  reverse.  At  the  quarters 
they  ought  to  be  equally  high,  but  unequal  in  their 
returns  ;  because  the  Earth's  axis  then  inclines  side- 


Of  the  Tides.  295 

wise  to  the  Moon.  In  winter,  the  phenomena  are 
the  same  at  full  Moon  as  in  summer  at  new.  In  au- 
tumn, the  Earth's  axis  inclines  sidewise  to  the  Moon 
when  new  and  full ;  therefore  the  tides  ought  to  be 
equally  high,  and  unequal  in  their  returns  at  these 
times.  At  the  first  quarter,  the  tides  of  flood  should 
be  least  when  the  Moon  is  above  the  horizon,  great- 
est when  she  is  below  it;  and  the  reverse  at  her  third 
quarter.  In  spring,  the  phenomena  of  the  first  quar- 
ter answer  to  those  of  the  third  quarter  in  autumn  ; 
and  vice  versa.  The  nearer  any  time  is  to  either  of 
these  seasons,  the  more  the  tides  partake  of  the  phe- 
nomena of  these  seasons ;  and  in  the  middle  between 
any  two  of  them,  the  tides  are  at  a  mean  state  be- 
tween those  "Df  both. 

308.  In  open  seas,  the  tides  rise  but  to  very  small  Why  the 
heights  in  proportion  to  what  they  do  in  wide-mouth-  ^erln 
ed  rivers,  opening  in  the  direction  of  the  stream  of  rivers  than 
tide.     For,  in  channels  growing  narrower  gradually, in  the  se* 
the  water  is  accumulated  by  the  opposition  of  the 
contracting  bank.     Like  a  gentle  wind,  little  felt  on 

an  open  plane,  but  strong  and  brisk  in  a  street;  es- 
pecially if  the  wider  end  of  the  street  be  next  the 
plane,  and  in  the  way  of  the  wind. 

309.  The  tides  are  so  retarded  in  their  passage  The  tides 
through  different  shoals  and  channels,  and  otherwise  ^diilian- 
so  variously  affected  by  striking  against  capes  and  ces  of  the 
headlands,  that  to  different  places  they  happen  at  all  ]^™nthe 
distances  of  the  Moon  from  the  meridian ;  conse-  meridian 
quently  at  all  hours  of  the  lunar  day.    The  tide  pro-  a*tdi^cre"s 
pagated  by  the  Moon  in  the  German  ocean  when  andPwhy.S' 
she  is  three  hours  past  the  meridian,  takes  12  hours 

to  come  from  thence  to  London-bridge  ;  where  it  ar- 
rives by  the  time  that  a  new  tide  is  raised  in  the 
ocean.  And  therefore  when  the  Moon  has  north  de- 
cimation, and  we  should  expect  the  tide  at  London 
to  be  greatest  when  the  Moon  is  above  the  horizon, 
we  find  it  is  least;  and  the  contrary  when  she  has 


260  Of  the  Tides. 

south  declination.  At  several  places  it  is  high-water 
three  hours  before  the  Moon  comes  to  the  meridian ; 
but  that  tide  which  the  Moon  pushes  as  it  were  be- 
fore her,  is  only  the  tide  opposite  to  that  which  was 
raised  by  her  when  she  was  nine  hours  past  the  op- 
posite meridian. 

The  water  310.  There  are  no  tides  in  lakes,  because  tbey 
hi  iakes!6Sare  generally  so  small,  that  when  the  Moon  is  verti- 
cal she  attracts  every  part  of  them  alike,  and  there- 
fore  by  rendering  all  the  water  equally  light,  no  part 
of  it  can  be  raised  higher  than  another.  The  Medi- 
terranean and  Baltic  seas  have  very  small  elevations, 
because  the  inlets  by  which  they  communicate  with 
the  ocean  are  so  narrow,  that  they  cannot  in  so  short 
a  time  receive  or  discharge  enough  to  raise  or  sink 
their  surfaces  sensibly. 

The  Moon     311.  Air  being  lighter  than  water,  and  the  sur- 
tkiesSinthe^ace  °^  ^e  atmosphere  being  nearer  to  the  Moon 
air.          than  the  surface  of  the  sea,  it  cannot  be  doubted 
that  the  Moon  raises  much  higher  tides  in  the  air 
than  in  the  sea.  And  therefore  many  have  wondered 
why  the  mercury  does  not  sink  in  the  barometer 
when  the  Moon's  action  on  the  particles  of  air  makes 
them  lighter  as  she  passes  over  the  meridian.     But 
Wh  the  we  must  consider,  that  as  these  particles  are  render- 
mercury    ed  lighter,  a  greater  number  of  them  is  accumulated, 
in  the  bar-  until  the  deficiency  of  gravity  be  made  up  by  the 
n^Tlffec*. height  of  the  column ;  and  then  there  is  an  eqmli- 
edbythe  brium,  and  consequently  an  equal  pressure  upon  the 
mercury  as  before ;  so  that  it  cannot  be  affected  by 
the  aerial  tides. 


Of  Eclipses.  261 


CHAP.  XVIII. 

Of  Eclipses:  Their  Number  and  Periods.    A  large 
Catalogue  of  Ancient  and  Modern  Eclipses. 

VERY  planet  and  satellite  is  illuminated  A  shadow 

by  the  Sun,  and  casts  a  shadow  toward  wliat* 
that  point  of  the  heavens  which  is  opposite  to  the 
Sun.  This  shadow  is  nothing  but  a  privation  of  light 
in  the  space  hid  from  the  Sun  by  the  opaque  body 
that  intercepts  his  rays. 

313.  When  the  Sun's  light  is  so  intercepted  by  Eclipses 
the  Moon,  that  to  any  place  of  the  Earth  the  Sun  °n^  MOOIJ 
appears  partly  or  wholly  covered,  he  is  said  to  un-  what. 
dergo  an  eclipse  ;  though,  properly  speaking,  it  is 
only  an  eclipse  of  that  part  of  the  Earth  where  the 
Moon's  shadow  or  *  penumbra  falls.  When  the 
Earth  comes  between  the  Sun  and  Moon,  the  Moon 
falls  into  the  Earth's  shadow  ;  and  having  no  light 
of  her  own,  she  suffers  a  real  eclipse  from  the  in- 
terception of  the  Sun's  rays.  When  the  Sun  is 
eclipsed  to  us,  the  Moon's  inhabitants  on  the  side 
next  the  Earth  (if  any  such  inhabitants  there  be)  see 
her  shadow  like  a  dark  spot  travelling  over  the  Earth, 
about  twice  as  fast  as  its  equatorial  parts  move,  and 
the  same  way  as  they  move.  When  the  Moon  is 
in  an  eclipse,  the  Sun  appears  eclipsed  to  her,  total 
to  all  those  parts  on  which  the  Earth's  shadow  falls, 
and  of  as  long  continue  as  they  are  in  the  shadow. 

3  14.  That  the  Earth  is  spherical  (for  the  hills  take  A  proof 
off  no  more  from  the  roundness  of  the  Earth,  than  that  the 


grains  of  dust  do  from  the  roundness  of  a  common     r     and 


arc 

globular 

*  The  penumbra  is  a  faint  kind  of  shadow  all  round  the  perfect  bodies. 
shadow  of  the  planet  or  satellite,  and  will  be  more  fully  explained 
bv  and  b\\ 


262  Of  Eclipses. 

globe)  is  evident  from  the  figure  of  its  shadow  oil 
the  Moon ;  which  is  always  bounded  by  a  circular 
line,  although  the  Earth  is  incessantly  turning  its  dif- 
ferent sides  to  the  Moon,  and  very  seldom  shews  the 
same  side  to  her  in  different  eclipses,  because  they 
seldom  happen  at  the  same  hours.     Were  the  Earth 
shaped  like  a  round  flat  plate,  its  shadow  would  only 
be  circular  when  either  of  its  sides  directly  faced  the 
Moon  ;  and  more  or  less  elliptical  as  the  Earth  hap- 
pened to  be  turned  more  or  less  obliquely  toward  the 
Moon  when  she  is  eclipsed.    The  Moon's  different 
phases  prove  her  to  be  round,  §  254 ;  for  as  she 
keeps  still  the  same  side  toward  the  Earth,  if  that 
side  were  flat,  as  it  appears  to  be,  she  would  never 
be  visible  from  the  third  quarter  to  the  first ;  and 
from  the  first  quarter  to  the  third,  she  would  appear 
as  round  as  when  we  say  she  is  full :  because  at  the 
end  of  her  first  quarter  the  Sun's  light  would  come 
as  suddenly  on  all  her  side  next  the  Earth,  as  it  does 
on  a  flat  wall,  and  go  off  as  abruptly  at  the  end  of 
her  third  quarter, 
and  that        315.  If  the  Earth  and  Sun  were  of  equal  magni- 

the  Sun  is  tudes.the  Earth's  shadow  would  be  infinitely  extend- 
much  Dig-      -  ,  .  r    .  ,.  J  ,     . 

gertban    ed,  and  every  where  ot  the  same  diameter;  and  the 
the  Earth,  planet  Mars,  in  either  of  its  nodes,  and  opposite  to  the 
Moon  e     Sun,  would  be  eclipsed  in  the  Earth's  shadow.  Were 
much  less,  the  Earth  bigger  than  the  Sun,  its  shadow  would  in- 
crease in  bulk  the  farther  it  extended,  and  would 
eclipse  the  great  planets  Jupiter  and  Saturn,  with  all 
their  moons,  when  they  were  opposite  to  the  Sun. 
But  as  Mars  in  opposition  never  falls  into  the  Earth's 
shadow,  although  he  is  not  then  above  42  millions 
of  miles  from  the  Earth,  it  is  plain  that  the  Earth  is 
much  less  than  the  Sun;  for  otherwise  its  shadow 
could  not  end  in  a  point  at  so  small  a  distance.     If 
the  Sun  and  Moon  were  of  equal  magnitude,  the 
Moon's  shadow  would  go  on  to  the  Earth  with  an 
equal  breadth,  and  cover  a  portion  of  the  Earth's  sur- 


Of  Eclipses.  263 

face  more  than  2000  miles  broad,  even  if  it  fell  di- 
rectly against  the  Earth's  centre,  as  seen  from  the 
Moon;  and  much  more  it  it  fell  obliquely  on  the 
Earth  :  but  the  Moon's  shadow  is  seldom  150  miles 
broad  at  the  Earth,  unless  when  it  falls  very  oblique- 
ly on  it  in  total  eclipses  of  the  Sun.  In  annular 
eclipses,  the  Moon's  real  shadow  ends  in  a  point  at 
some  distance  from  the  Earth.  The  Moon's  small 
distance  from  the  Earth,  and  the  shortness  of  her 
shadow,  prove  her  to  be  less  than  the  Sun.  And 
as  the  Earth's  shadow  is  large  enough  to  cover  the 
Moon,  if  her  diameter  were  three  times  as  large  as 
it  is  (which  is  evident  from  her  long  continuance  in 
the  shadow  when  she  goes  through  its  centre)  it  is 
plain  that  the  Earth  is  much  larger  than  the  Moon. 

316.  Though  all  opaque  bodies  on  which  the  Sun  The  pri- 
shines  have  their  shadows,  yet  such  is  the  bulk  of  ™*rypj^j' 
the  Sun,  and  the  distances  of  the  planets,  that  the  eclipse 
primary  planets  can  never  eclipse  one  another.     A  one  ano- 
primary  can  eclipse  only  its  secondaries  or  be  eclips- 
ed by  them ;  and  never  but  when  in   opposition  to, 

or  conjunction  with,  the  Sun.  The  Sun  and  Moon 
are  so  every  month :  whence  one  may  imagine  tkat 
these  two  luminaries  should  be  eclipsed  every  month. 
But  there  are  few  eclipses  in  respect  to  the  number 
of  new  and  full  Moons ;  the  reason  of  which  we 
shall  now  explain. 

317.  If  the  Moon's  orbit  were  coincident  with  Why 
the  plane  of  the  ecliptic,  in  which  the  Earth  always  ^few"^ 
moves,  and  the  Sun  appears  to  move,  the  Moon's  eclipses, 
shadow  would  fall  upon  the  Earth  at  every  change, 

and  eclipse  the  Sun  to  some  parts  of  the  Earth.  In 
like  manner,  the  Moon  would  go  through  the  raid- 
die  of  the  Earth's  shadow,  and  be  eclipsed  at  every 
full ;  but  with  this  difference,  that  she  would  be 
totally  darkened  for  above  an  hour  and  an  half;  where- 
as the  Sun  never  was  above  four  minutes  totally 
eclipsed  by  the  interposition  of  the  Moon.  ButoneThe 
half  of  the  Moon's  orbit  is  elevated  5~  degrees  above  Moon's 

T     i  nodes, 


264  Of  Eclipses. 

the  ecliptic,  and  the  other  half  as  much  depressed 
below  it :  consequently  the  Moon's  orbit  intersects 
the  ecliptic  in  two  opposite  points  called  the  Moon's 
nodes,  as  has  been  already  taken  notice  of,  §  288. 
When  these  points  are  in  a  right  line  with  the  cen- 
tre of  the  Sun  at  new  or  full  Moon,  the  Sun,  Moon, 
and  Earth,  are  all  in  a  right  line ;  and  if  the  Moon 
be  then  new,  her  shadow  falls  upon  the  Earth ;  if 
Limits  of  full,  the  Earth's  shadow  falls  upon  her.  #  When  the 
echpses.  Sun  and  Moon  are  more  than  17  degrees  from  ei- 
ther of  the  nodes  at  the  time  of  conjunction,  the 
Moon  is  then  generally  too  high  or  too  low  in  her 
orbit  to  cast  any  part  of  her  shadow  upon  the  Earth. 
And  when  the  Sun  is  more  than  twelve  degrees  from 
either  of  the  nodes  at  the  time  of  full  Moon,  the 
Moon  is  generally  too  high  or  too  low  in  her  orbit  to 
go  through  any  part  of  the  Earth's  shadow :  and  in 
both  these  cases  there  will  be  no  eclipse.  But  when 
the  Moon  is  less  than  17  degrees  from  either  node 
at  the  time  of  conjunction,  her  shadow  or  penum- 
bra falls  more  or  less  upon  the  Earth,  as  she  is: more 
or  less  within  this  limit.-  And  when  she  is  less 
than  12  degrees  from  either  node  at  the  time  of  op- 
position, she  goes  through  a  greater  or  less  portion 
of  the  Earth's  shadow  as  she  is  more  or  less  within 
this  limit.  Her  orbit  contains  360  degrees,  of  which 
17,  the  limit  of  solar  eclipses  on  either  side  of  the 
nodes,  and  12,  the  limit  of  lunar  eclipses,  are  but 
small  portions  :  and  as  the  Sun  commonly  passes  by 
the  nodes  but  twice  in  a  year,  it  is'no  wonder  that 
we  have  so  many  new  and  full  Moons  without 
eclipses. 


*  Tliis  admits  of  some  variation :  for  in  apogeal  eclipses,  the 
solar  limit  is  hut  16  1-2  degrees ;  and  in  perigeal  eclipses,  it  is  18 1-3. 
When  tiie  full  Moon  is  in  her  apogee,  she  will  be  eclipsed  if  she  be 
within  10 1-2  degrees  of  the  node  ;  and  when  she  is  full  in  her  pe- 
rigee, she  will  be  eclipsed  if  she  be  within  12-^  degrees  of  the 
node. 


Of  Eclipses.  265 

To  illustrate  this,  let  A  B  C  D  be  the  eliptic,  *LATE 
It  S  T  £7  a  circle  lying  in  the  same  plane  with  the 
ecliptic,  and  VWXYfat  Maoris  orbit,  all  thrownFi£-  L 
into  an  oblique  view,  which  gives  them  an  elliptical 
shape  to  the  eye.     One  half  of  the  Moon's  orbit,  as 
V  W  X,  is  always  below  the  ecliptic,  and  the  other 
half  X  Y  7  above  it.    The  points  Tand  X,  where 
the  Moon's  orbit  intersects  the  circle  R  S  T  U, 
which  lies  even  with  the  ecliptic,  are  the  Mooris 
nodes  ;  and  a  right  line,  as  X]£P9  drawn  from  one  Lines  of 
to  the  other,  through  the  Earth's  centre,  is  called the  nodes* 
the  Line  of  the  nodes,  which  is  carried  almost  pa- 
rallel to  itself  round  the  Sun  in  a  year. 

If  the  Moon  moved  round  the  Earth  in  the  orbit 
R  S  T  U,  which  is  coincident  with  the  plane  of  the 
ecliptic,  her  shadow  would  fall  upon  the  Earth  eve- 
ry time  she  is  in  conjunction  with  the  Sun,  and  at 
every  opposition  she  would  go  through  the  Earth's 
shadow.  Were  this  the  case,  the  Sun  would  be 
eclipsed  at  every  change,  and  the  Moon  at  every 
full,  as  already  mentioned. 

But  although  the  Moon's  shadow  A" must  fall  up- 
on the  Earth  at  a,  when  the  Earth  is  at  E,  and  the 
Moon  in  conjunction  with  the  Sun,  at  i,  because 
she  is  then  very  near  one  of  her  nodes,  and  at  her 
opposition  n,  she  must  go  through  the  Earth's  sha- 
dow /,  because  she  is  then  near  the  other  node ;  yet, 
in  the  time  that  she  goes  round  the  Earth  to  her  next 
change  according  to  the  order  of  the  letters  X  Y  V 
W,  the  Earth  advances  from  E  to  c,  according  to 
the  order  of  the  letters  E  F  G  If,  and  the  line  of 
the  nodes  VEX  being  carried  nearly  parallel  to  it- 
self, brings  the  point  /of  the  Moon's  orbit  in  con- 
junction  with  the  Sun  at  that  next  change  ;  and  then 
the  Moon  being  at/  is  too  high  above  the  ecliptic  to 
cast  her  shadow  on  the  Earth :  and  as  the  Earth 
is  still  moving  forward,  the  Moon  at  her  next  op- 
position will  be  at  g,  too  far  belowr  the  ecliptic  to 


266  Of  Eclipses. 

PLATE  gO  through  any  part  of  the  Earth's  shadow;  for  by 
that  time  the  point  g  will  be  at  a  considerable  dis- 
tance from  the  Earth  as  seen  from  the  Sun. 

When  the  Earth  comes  to  F,  the  Moon  in  con- 
junction with  the  Sun  Z  is  not  at  &,  in  a  plane  coinci- 
dent with  the  ecliptic,  but  above  it  at  Y  in  the  high- 
est part  of  her  orbit :  and  then  the  point  b  of  her 
shadow  0  goes  far  above  the  Earth  (as  in  Fig.  II. 
rig.  i.  which  is  an  edge-view  of  Fig.  I.)  The  Moon  in  her 
*nd  IL  next  opposition  is  not  at  o  (Fig.  I.)  but  at  W,  where 
the  Earth's  shadow  goes  far  above  her  (as  in  Fig. 
II.)  In  both  these  cases  the  line  of  the  nodes  V  FX 
(Fig.  I.)  is  about  90  degrees  from  the  Sun,  and  both 
luminaries  are  as  far  as  possible  from  the  limits  of 
eclipses. 

When  the  Earth  has  gone  half  round  the  eclip 
tic  from  E  to  G,  the  line  of  the  nodes  V  G  X  is 
nearly,  if  not  exactly,  directed  towards  the  Sun  at 
Z ;  and  then  the  new  Moon  /  casts  her  shadow  P 
on  the  Earth  G;  and  the  full  Moon/?  goes  through 
the  Earth's  shadow  L  ;  which  brings  on  eclipses 
again,  as  when  the  Earth  \vas  at  E. 

When  the  Earth  comes  to  H,  the  new  Moon  falls 
not  at  m  in  a  plane  coincident  with  the  ecliptic  CD, 
but  at  JV  in  her  orbit  below  it :  and  then  her  sha- 
dow Q  (see  Fig.  II.)  goes  far  below  the  Earth.  At 
the  next  full  she  is  not  at  q  (Fig.  I.)  but  at  Fin  her 
orbit  5^  degrees  above  q,  and  at  her  greatest  height 
above  the  ecliptic  CD;  being  then  as  far  as  possi- 
ble, at  any  opposition,  from  the  Earth's  shadow  M 
(as  in  Fig.  II.) 

So,  when  the  Earth  is  at  E  and  G,  the  Moon  is 
about  her  nodes  at  new  and  full ;  and  in  her  greatest 
north  and  south  declination  (or  latitude  as  it  is  gene- 
rally called)  from  the  ecliptic  at  her  quarters:  but 
when  the  Earth  is  at  F  or  H,  the  Moon  is  in  her 
greatest  north  and  south  declination  from  the  ecliptic 
fit  new  and  full,  and  in  the  nodes  about  her  quarters, 


Of  Eclipses.  267 


PLATE 
X. 


318.  The  point  X  where  the  Moon's  orbit  cros- 
ses the  ecliptic  is  called  the  ascending  node,  because 

the  Moon  ascends  from  it  above  the  ecliptic  :  and  JJj,®  n»s 
the  opposite  point  of  intersection  F"\s  called  the  de-  ascending 
scending  ?iode,  because  the  Moon  descends  from  it 
below  the  ecliptic.     When  the  Moon  is  at  F  in  the 
highest  point  of  her  orbit,  she  is   in  her  greatest 
north  latitude :  and  when  she  is  at  /Fin  the  lowest  and south 
point  of  her  orbit,  she  is  in  her  greatest  south  lati-  latitude. 
tude. 

319.  If  the  line  of  the  nodes,  like  the  Earth's  ax-  The  nodes 
is,  were  carried  parallel  to  itself  round   the  Sun,  {£^dj*" 
there  would  be  just  half  a  year  between  the  conjunc-  motion, 
lions  of  the  Sun  and  nodes.     But  the  nodes  shift 
backward,  or  contrary  to  the  Earth's  annual  motion, 

19- degrees  every  year;  and  therefore  the   sameFjg>  L 
node  comes  round  to  the  Sun  19  days  sooner  every 
year  than  on  the  year  before.     Consequently,  from 
the  time  that  the  ascending  node  X  (when  the  Earth 
is  at£J  passes  by  the  Sun,  as  seen  from  the  Earth, 
it  is  only  173  days  (not  half  a  year)  till  the  descend- 
ing node  V  passes  by  him.     Therefore,  in  whatever 
time  of  the  year  we  have  eclipses  of  the  luminaries  the  eciips- 
about  either  node,  we  may  be  sure  that  in  173days^esroon^r 
afterward,  we  shall  have  eclipses  about  the  other  than  they 
node.     And  when  at  any  time  of  the  year  the  line  of  ^°ha(Jd  be 
the  nodes  is  in  the  situation  V  G  Jf,  at  the  same  time  nodes  had 
next  year  it  will  be  in  the  situation  r  G  s ;  the  as-  not  fuch  a 
cending  node  having  gone  backward,  that  is,  contra- m 
ry  to  the  order  of  signs,  from  X  to  s,  and  the  de- 
scending node  from  Ftor-,  each  19-i  degrees.     At 
this  rate  the  nodes  shift  through  all  the  signs  and  de- 
grees of  the  ecliptic  in  18  years  and  225  days;  in 
which  time  there  would  always  be  a  regular  period 
of  eclipses,  if  any  complete  number   of  lunations 
were  finished  without  a  fraction.      But  this  never 
happens ;    for  if  both  the  Sun  and  Moon  should 
start  from  a  line  of  conjunction  with  either  of  the 
nodes  in  any  point  of  the  ecliptic,  the  Sun  would 


268  Of  Eclipses. 

perform  18  annual  revolutions  and  222  degrees  over 
and  above,  and  the  Moon  230  lunations  and  85  de- 
grees of  the  231st,  by  the  time  the  node  came  round 
to  the  same  point  of  the  ecliptic  again;  so  that  the 
Sun  would  then  be  138  degrees  from  the  node,  and 
the  Moon  85  degrees  from  the  Sun. 

A  period  320.  But,  in  223  mean  lunations,  after  the  Sun, 
o^ec  ips-  ^|oon^  amj  no(jeS)  have  been  once  in  a  line  of  con- 
junction, they  return  so  nearly  to  the  same  state 
again,  as  that  the  same  node,  which  was  in  conjunc- 
tion with  the  Sun  and  Moon  at  the  beginning  of  the 
first  of  these  lunations,  will  be  within  28'  12"  of  a 
degree  of  a  line  of  conjunction  with  the  Sun  and 
Moon  again,  when  the  last  of  these  lunations  is 
completed.  And  therefore,  in  that  time,  there  will 
be  a,  regular  period  of  eclipses,  or  return  of  the 
same  eclipse  for  many  ages. — In  this  period,  (which 
was  first  discovered  by  the  Chaldeans  J  there  are  18 
Julian  years  11  days  7  hours  43  minutes  20  seconds, 
when  the  last  day  of  February  in  leap-years  is  four 
times  included :  but  when  it  is  five  times  included, 
the  period  consists  of  only  18  years  10  days  7  hours 
43  minutes  20  seconds.  Consequently,  if  to  the 
mean  time  of  any  eclipse,  either  of  the  Sun  or 
Moon,  you  add  IS  Julian  years  11  days  7  hours  43 
minutes  20  seconds,  when  the  last  day  of  Februa- 
ry in  leap-years  comes  in  four  times,  or  a  day  less 
when  it  comes  in  five  times,  you  will  have  the  mean 
time  of  the  return  of  the  same  eclipse. 

But  the  falling-back  of  the  line  of  conjunctions 
or  oppositions  of  the  Sun  and  Moon  2J8'  12"  ^vith 
respect  to  the  line  of  the  nodes  in  every  period,  will 
wear  it  out  in  process  of  time  ;  and  after  that,  it  will 
not  return  again  in  less  than  12492  years. — These 
eclipses  of  the  Sun,  which  happen  about  the  ascend- 
ing node,  and  begin  to  come  in  at  the  north  pole 
of  the  Earth,  will  go  a  little  southerly  at  each  re- 
turn, till  they  -go  quite  off  the  Earth  at  the  south 


Of  Eclipses.  269 

pole ;  and  those  which  happen  about  the  descending 
node,  and  begin  to  come  in  at  the  south  pole  of  the 
Earth,  will  go  a  little  northerly  at  each  return,  till 
at  last  they  quite  leave  the  Earth  at  the  north  pole. 

To  exemplify  this  matter,  we  shall  first  consider 
the  Sun's  eclipse,  March  21st  old  stile  (April  1st 
new  stile)  A.  D.  1764,  according  to  its  mean  revolu- 
tions, without  equating  the  times,  or  the  Sun's  dis- 
tance from  the  node ;  and  then  according  to  its  true 
equated  times. 

This  eclipse  fell  in  the  open  space  at  each  return, 
quite  clear  of  the  Earth,  from  the  creation  till 
A.  D.  1295,  June  13th  old  stile,  at  12  h.  52  m.  59 
sec.  post  meridiem^  when  the  Moon's  shadow  first 
touched  the  Earth  at  the  north  pole ;  the  Sun  being 
then  17°  48'  27"  from  the  ascending  node. — In 
each  period  since  that  time,  the  Sun  has  come  28' 
12"  nearer  and  nearer  the  same  node,  and  the 
Moon's  shadow  has  therefore  gone  more  and  more 
southerly. — Indie  year  1962,  July  18th old  stile,  at 
10  h.  36  m.  21  sec.  p.  m.  when  the  same  eclipse  will 
have  returned  38  times,  the  Sun  will  be  only  24' 
45"  from  the  ascending  node,  and  the  centre  of  the 
Moon's  shadow  will  fall  a  little  northward  of  the 
Earth's  centre. — At  the  end  of  the  next  following 
period,  A.  D.  1980,  July  28th  old  stile,  at  18  h. 
19  m.  41  sec.  p.  m.  the  Sun  will  have  receded  back 
3'  27"  from  the  ascending  node,  and  the  Moon  will 
have  a  very  small  degree  of  southern  latitude,  which 
will  cause  the  centre  of  her  shadow  to  pass  a  very 
small  matter  south  of  the  Earth's  centre. — After 
which,  in  every  following  period,  the  Sun  will  be 
28'  12"  farther  back  from  the  ascending  node  than 
in  the  period  last  before ;  and  the  Moon's  shadow- 
will  go  still  farther  and  farther  southward,  un- 
til September  12th old  stile,  at  23  h.  46  m.  22  sec. 
p.  m.  A.  D.  2665;  when  the  eclipse  will  have  com- 
pleted its  77th  periodical  return,  and  will  go  quite 
off  the  Earth  at  the  south  pole  (the  Sun  being  then 


270  Of  Eclipses. 

17°  55'  22"  back  from  the  node) ;  and  it  cannot 
come  in  from  the  north  pole,  so  as  to  begin  the  same 
course  over  again,  in  less  than  12492  years  after- 
ward.— And  such  will  be  the  case  of  every  other 
eclipse  of  the  Sun  :  for,  as  there  is  about  1 8  degrees 
on  each  side  of  the  node  within  which  there  is  a 
possibility  of  eclipses,  their  whole  revolution  goes 
through  36  degrees  about  that  node,  which,  taken 
from  360  degrees,  leaves  remaining  324  degrees  for 
the  eclipses  to  travel  in  expamum.  And  as  these 
36  degrees  are  not  gone  through  in  less  than  77  pe- 
riods, which  take  up  1388  years,  the  remaining  324 
degrees  cannot  be  so  gone  through  in  less  than  12492 
years.  For  as  36  is  to  1388,  so  is  324  to  12492. 

321.  In  order  to  shew  both  the  mean  and  true 
times  of  the  returns  of  this  eclipse,  through  all  its 
periods,  together  with  the  mean  anomalies  of  the 
Sun  and  Moon  at  each  return,  and  the  mean  and 
true  distances  of  the  Sun  from  the  Moon's  ascend- 
ing node,  and  the  Moon's  true  latitude  at  the  true 
time  of  each  new  Moon,  I  have  calculated  the  fol- 
lowing tables  for  the  sake  of  those  who  may  choose 
to  project  this  eclipse  at  any  of  its  returns,  accord- 
ing to  the  rules  laid  down  in  the  X Vth  chapter ;  and 
have  by  that  means  taken  by  much  the  greatest  part 
of  the  trouble  off  their  hands. — All  the  times  are  ac- 
cording to  the  old  stile,  for  the  sake  of  a  regularity 
which,  with  respect  to  the  nominal  days  of  the 
months,  does  not  take  place  in  the  new  :  but  by  add- 
ing the  days  difference  of  stile ;  they  are  reduced  to 
the  times  which  agree  with  the  new  stile. 

According  to  the  mean  (or  supposed)  equable  mo- 
tions  of  the  Sun,  Moon,  and  nodes,  the  Moon's 
shadow  in  this  eclipse  would  have  first  touched  the 
Earth  at  the  north  pole,  on  the  13th  of  June,  A.  D. 
1295,  at  12  h.  52m.  59  sec.  past  noon  on  the  meri- 
dian of *  London;  and  would  quite  leave  the  Earth  at  the 


Of  Eclipses.  271 

south  pole,  on  the  12th  of  September,  A.  D.  2665, 
.at  23  h.  46  m.  22  sec.  past  noon,  at  the  completion 
of  its  77th  period;  as  shewn  by  the  first  and  second 
tables. 

But,  on  account  of  the  true  or  unequable  motions 
of  the  Sun,  Moon,  and  nodes,  the  first  coming  in 
of  this  eclipse,  at  the  north  pole  of  the  .^arth,  was 
on  the  24th  of  June,  A.  D.  1313,  at  3  h.  57  m.  3 
sec.  past  noon ;  and  it  will  finally  leave  the  earth  at 
the  south  pole,  on  the  31st  of  July,  A.  D.  2593,  at 
10  h.  25  m.  31  sec.  past  noon,  at  the  completion  of 
its  72d  period ;  as  shewn  by  the  third  and  fourth  ta- 
bles.— So  that  the  true  motions  do  not  only  alter 
the  true  times  from  the  mean,  but  they  also  cut  off 
five  periods  from  those  of  the  mean  returns  of  this 
eclipse. 


Mm 


272 


Of  E 


<J  TABLE  I.      The  mean  time  of  New  Afoon,  with  the  mean  Anomalies  of  the  ? 
Sun  and  Moon,  and  the  Sun's  mean  Distance  from  the  Moon's  Ascending  * 
J&rde,  at  the  mean  time   of  each  periodical  Return  of  the  Sun's  Eclifise, 
March  21st,  I764n/rom  its  first  coming  ufion  the  Earth  since  the  crea- 
ation,  till  it  falls  right  against  the  Earth's  centre,  according  to   the  Old 


Periodical 
1  Returns. 

f  o 

Meantime  of 
New  'Moon. 

Sun's  mean 
Anomaly. 

Moon's  mean  KSun'smeandisf  ^ 
Anomaly,  'from  the  Node  s 

Month.  D.  H.  M.S. 

s.  0.  '  " 

-s.  o.  '  " 

s.  0.  '     S 

0 

1277 

June   2  5  9  39 

il  17  57  41 

1  26  31  42 

0  18  16  40  S 

1 

1295 

June  13  12  52  59 

11  28  27  38 

1  23  40  19 

0  17  48  27 

o 

1313 

June  23  20  36  19 

0  8  57  35 

1  20  48  56 

0  17  20  15 

3 

1331 

July   5  4  19  30 

0  19  27  32 

1  17  57  35 

0  16  52  2 

4 

1349 

July  15  12  2  59 

0  29  57  29 

1  15   6  10 

0  16  23  50  * 

5 

136-7 

July  26  19  46  19 

1  10  27  26 

12  14  47 

0  15  55  37  \ 

6 

1385 

:\ug.  6  3  29  39 

1  20  57  2"3 

9  23  24 

0  15  27  25 

7 

1403 

Aug.  17  11  12  59 

2   1  27  20 

6  32   1 

0  14  59  12 

8 

1421 

Aug.  27  18  56  19 

2  11  57  17 

3  40  38 

0  14  31  0 

9 

1439 

Sept.  8  2  39  39 

2  22  27  14 

1   0  49  15 

0  14  2  47 

LO 

1457 

Sept.  18  10  2  59 

3  2  57  11 

0  27  57  52 

0  13  34  35 

LI 

^1475 

Sept.  29  18  6  19 

3  13  27  8 

0  25  6  29 

0  13  6  22 

L2 

1493 

Oct.  10   1  49  39 

3  23  57  5 

0  22  15   6 

0  12  38  10 

13 

1511 

Oct.  21  9  32  59 

4  4  27  2 

0  19  23  43 

0  12  9  57 

14 

1529 

Oct.  31  17  16  19 

4  14  56  59 

0  16  32  20 

:  0  11  41  45  J 

15 

154:7 

Nov.  12  0  59  40 

4  25  26  56 

0  13  40  57 

Oil  13  32  ? 

16 

150.) 

Nov.  22  8  43  0 

5   5  56  53 

0  10  49  34 

0  10  45  20  J 

17 

1583 

Dec.   3  16  26  20 

5  16  26  50 

0  7  58  9 

0  10  17  7  \ 

8 

1601 

Dec.  14  0  9  40 

5  26  56  47 

O  5  6  48 

0  9  48  55  J 

9 

1619 

Dec.  25  7  53  0 

6  7  26  44 

0  2  15  25 

O  9  20  42  ^ 

10 

1638 

Jan.   4  15  36  20 

6  17  56  41 

11  29  24  2 

0  8  52  30  > 

11 

1656 

Jan.  15  23  19  40 

6  28  26  38 

11  26,  32  39 

0  8  24  17  S 

11 

1674 

Jan.  26  7  3  0 

7  8  56  35 

1  23  41  14 

0  7  56  5  £ 

J3 

1692 

Feb.   6  14  46  20 

7  19  26  32 

20  49  53 

0  7  27  52  £ 

14 

1710 

Feb.  16  22  29  40 

7  29  56  29 

17  58  30 

0  6  59  40  Jj 

15 

1728 

Feb.  28  6  13  0 

8  10  26  26 

15  7  7 

0  6  31  27  ? 

-6 

1746 

Mar.  10  13  56  20 

8  20  56  23 

12  15  44 

0  6  3  15  > 

17 

1764 

Mar.  20  21  39  40 

9   1  26  20 

9  24  21 

0  5  35  2S 

HB 

1782 

Apr.   1  5  23  0 

9  11  56  17 

6  32  58 

0  5  6  50  Jj 

9 

1800 

Apr.  11  13  6  20 

9  22  26  14 

3  41  35 

0  4  38  37  S 

»0 

1818 

Apr.  22  20  49  40 

10  2  56  11 

0  50  12 

0  4  10  25  \ 

1 

1836 

Vlay   3  4  33  0 

10  13  26  8 

10  27  58  49 

0  3  42  12  Ij 

2 

1854 

May  14  12  16  20 

10  23  56  5 

10  25   7  26 

0  3  14  0  S 

3 

1872 

May  24  19  59  40 

11   4  26  2 

10  22  16  3 

0  2  45  47  !j 

4 

1890 

June  5  3  43  0 

11  14  55  59 

10  19  24  40 

0  2  17  35  S 

5 

1908 

June  15  11  26  20 

11  25  25  56 

10  16  33  17 

0   1  49  22  £ 

6 

1926 

June  26  19  9  40 

0   5  55  53 

10  13  41  54 

0   1  21  10  S 

7 

1944 

July   7  2  53  0 

0  16  25  50 

10  10  50  31 

0  0  52  57  ^ 

8 

1962 

July  18  10  36  21 

0  26  55  47 

10  7  59   8 

0  0  24  45  > 

JL. 

Of  Eclipses. 


TABLE  II.  The  mean  time  of  New  Moon,  with  the  mean  Anomalies  of  the  S 
Sun  and  Moon,  and  the  Sun's  mean  Distance  from  the  Moon's  dscend-  s 
ing  Node,  at  the  mean  Time  of  each  periodical  Return  of  the  Sun' a  S 
Eclipse,  March  21«f,  1764,  from  the  mean  Time  of  its  falling  riifht  £ 

•  j  »  J^  .   f   »  X~»  .',,-.*  •*  O  O  } 


the  Julian,  or  Old  Style.                                                                                       ^ 

|l 

2T  ?' 

Mean  time  oi 
New  Moon. 

Sun's  mean 
Anomaly. 

Moon's  mean 
Anomaly. 

Sun's  mean  (list.  £ 
from  the  Node.   ^ 

if 

Month.  D.H.M.S. 

s.    0.    '       ' 

s.     o.     '     " 

s    0.     '     "       S 

^ 

19b- 

ju,y    28   18   19  41 

1        7    *o    44.  1U     5      7    45 

1  1    -«j  5o  38     Jj 

40 

1998 

Aug,    9231 

1     17    55    41  10     2  16   22 

11    29  23  20    S 

41 

2016 

Aug.  19     9  46  2 

I    28    25    38    9  29  24    59 

11    29     0     8     £ 

42 

2034 

Aug.  SO  17  29.41 

2      8    53    36    9  26  33   36 

11    28  31  55     S 

43 

3052 

Sept.  10     1  13     1 

2    19    25    33     9  23  42    13 

1128     343     Ij 

44 

2070 

Sept.  21     8  56  21 

2    29    55    32     9  20  50    50 

11    27  35  30    S 

45 

2088 

Oct.       1  16  39  41 

3    10    25    27    9  17  59    27 

11    27     7  18     £ 

46 

2106 

Oct.    13     0  23     1 

3   20    55  24    9  15     8      4 

11    26  39     5     S 

47 

2124 

Oct.    2.3     8     621 

4       1    25   21     9  12   16  41 

11    26   10  53    Jj 

48 

2142 

Nov.      3  154941 

4    1  1    55    18     9     9  25    18 

11    25  42  40    S 

49 

2160 

Nov.    13  23  31     1 

4   22    25    15     9     6  33  36 

11    25   14  28    Jj 

50 

2178 

Nov,    25     71621 

5      2    55    12     9     3  42    33 

11    24  46  15    S 

51 

2196 

Dec.      5  14  59  41 

5    13    25      9     9     0  51    10 

11    24   18     3    % 

52 

2214 

De<:.    16  22  43     1 

5    23    55      7    8  27  59   47 

11    23  49  50    S 

53     ' 

2232 

Dec.    27     6  26  21 

6      4   25      4[  8  25     8   24 

11    23  21  38    £ 

54 

2251 

Jan.       7  14    9  41 

6    14   55      1 

8  22  17      1 

11    22  53  25    S 

55 

2269 

Jan.     17  21  53     1 

6   25    24   58 

8  19  2,5   38 

11    22   15  13    ^ 

56 

2287 

Jan,     29     5  36  21 

7      5    54   55 

8  d6  31    15 

11    21  57    0    S 

57 

2305 

Feb.      -8  13  19  41 

7    16   24   52 

8  13  42   52 

11    21  28  48    5 

58 

2323 

Feb.    19  21     3     1 

7   26    54   49 

8  10  51    29 

11    21     0  35     S 

59 

2341 

Mar.     2     44621 

8      7    24   46 

8806 

11    20  32  23    !j 

60 

2359 

Mar.    13  12  29  42 

8    17    54   43 

8     5     8   43 

11    20     4  10    S 

61 

2377 

Mar.  23  20  13     2 

8    28    24  40 

8     2  17    20 

11    19  35  58     ^ 

62 

2395 

Apr.     4     3  56  22 

9      8    54   37 

7  29  25    27 

11    19     7  45     S  ' 

63 

2413 

Apr.    14  11  39  42 

9    19    24   34 

7  26  34   34 

11    18  39  S3    Jj 

64 

2431 

Apr.  2.5   19  23     2 

9    29    54   31 

7  23  43    11 

11    18   11  20    S 

65 

2449 

May     6     3     0  22 

10    10    24   28 

7  20  51    48 

11    17  43     8    £: 

66 

2467 

May    17   10  49  42 

10   20    54   25 

7   18     0   25 

11    17   14  54     S  '' 

67 

2485 

May   27  18  33     2 

11       1    24    22 

7   15     9      2 

11    16  46  43     ? 

68 

2503 

June     8     21622 

11    11    54    19 

7  12  17    39 

11    16  18  31     S 

69 

2521 

June   18     9  59  42 

11    22    24    17 

7     9  26    16 

11    15  50  18     Ij 

70 

2539 

June  29  17  43    2 

0      2    54    14 

7     6  34   53 

11    15  22     6    < 

71 

2557 

July    10     1  26  22 

0    13    24    11 

7     3  44   30 

11    14  53  54    ^! 

72 

2575 

July    21     9     9  42 

0   23    54      8 

7     0  52      7 

11    14  25  41     V 

73 

2593 

July    31  16  53    2 

1      4    24      5 

6  28     0   44 

11    13  57  28    y 

74 

2611 

Aug.  12     0  36  22 

1    14    54      2 

6  25     921 

11    13  29  16    S 

75 

2629 

Aug.  22     8  19  42 

1    25    23    59 

6  22  17   58 

11    13     1     3    Jj 

76 

2647 

Sept.     2  16     3    2 

2      5    53    56 

6  19  26    35 

11    12  32  51     S 

77 

2665 

Sept.  12  23  46  22 

2    16    23   53 

6  16  35    12 

11    12     4  38    ^ 

274 


Of  Eclipses. 


S  TABLE  III.   The  true  Time  of  New  Moon,  with  the  Sun's  truc\ 

?       Distance  from  the  Moon's  Ascending  Node,  and  the  Moon's  true  v> 

S       Latitude,  at  the  true  Time  of  each  periodical  Return  of  the  Sun's  S 

^      Eclipse,  March  2\st,  Old  Style,  A.  D.  \7  64,  from  the  Time  o/«J 

S       itsjirst  coining  upon  the  Earth  since  the   Creation  till  it  falls  J» 

^      right  against  the  Earth's  Centre.                                                       ^ 

5  »3F 

—  »•< 

True  lime  of 

>un'strueDist. 

Moon's  true  Lati-  Jj 

<  a  S 
s  £  s 

t    a  p.-. 

i§ 

WJ*    ^ 

New  Moon. 

rom  the  Node. 

tude  North. 

t 

$  y  ? 

.-"  o 

Month.l).  H.M.  S. 

s.  .0      '      " 

0.    '       "     Nor.  S 

5   o 

i295 

June   13    12  54  32 

0    18   40    54 

1    33   45   N.   A.  s 

S     i 

1313 

June  24     3  57     3 

0    17   20    22 

1    29    84  N.   A.  J 

5     2 

1331 

July      5    10  42     8 

0    16   29    35 

1    25    20   N.   A.  s 

J    3 

-1349 

July      15    17    14    15 

0    15    34    18 

1    20    45    N.   A.  £ 

•;  4 

1367 

July    26  23  49   24 

0    14   46      8 

1    16    39    N.   A.s 

$  * 

1385 

Aug.     6      6  41    17 

0    13    59    43 

2    12   43   N.   A.  S 

\  6 

1403 

Aug.    17    13   32    19 

0    13    16   44 

1      9      3   N.   A.  s 

5  t 

1421 

Aug    27  20  30   17 

0    12    37      4 

1      5   42   N.  A.  S 

J     8 

4439 

Sept.     8     3  51   46 

0    12      1    54 

1      2   41    N.   A.  s 

5     9 

1457 

Sept    18    10  23    11 

0    11    30   27 

0   58    33  N.   A.  S 

5  io 

1475 

Sept.  29    17  57     7 

0    11      3    56 

0   57   43   N.   A.  s 

I'ii 

1493 

Oct.     16      1   44     3 

0    10   41    55 

0    55    49    N.   A.  £ 

$12 

1511 

Oct.    21      9  29   53 

0    10   25    11 

0   54   28   N.   A.  ^ 

$13 

1529 

Oct.    31    17     9    18 

0    10    11    27 

0    53    12   N.   A.  S 

5» 

1547 

Nov.    12     0  51    25 

0    10      1    10 

0    52    19    N.   A.  < 

5  15 

1565 

Nov.    22     8  54   56 

0     9    52   49 

0    51    46   N.   A.  > 

i»« 

1583 

Dec.      3   16  48    17 

0     9   48      4 

0   51    11   N.  A.  ^ 

sir 

1601 

Dec.      4     0  51      5 

0     9   43   42 

0   50   49    N.    A.  J> 

$18 

1619 

Dec.    25      8   54  59 

0     9   40   23 

0   50   31    N.   A.  s 

I19 

1638 

Jan.       4    16  56     1 

0     9    34   57 

0   50     3   N.  A.  S 

<  20 

1556 

Jan.      16     0  54  41 

0      9    29    24 

0   49    57    N.   A.  s 

$21 

1674 

Jan.     26     S  48   24 

0      9    19    44 

0   48   44   N.   A.  S 

\  22 

1692 

Feb.      6    16   36    28 

0     9      8    5S 

0  47  49   N.   A.  s 

^  23 

1710 

Feb.    17     0     8    37 

0      g    54   20 

0  46   44  N.   A.  S 

5  24 

.728 

Feb.    28      7  43    40 

0      S    34    53 

0   44   52    N.   A.  s 

^25 

1746 

Mar.    10    15    14    3- 

0      8    10    38 

0   42    46    N.    A.  S 

$26 

1764 

Mar.  20  22   30   26 

0      7    42    14 

0   40    18    N.   A.  s 

$27 

1782 

Apr.      1     5   37     4 

0      7      9    27 

0   37   28   N.  A.  S 

S  „„ 
S  ^8 

1800|Apr.    11    12   36   38 

0      6    35    30 

0   34   31    N.   A.  <J 

S  29 

ISIS 

Apr.    22    19  27   34 

0      5    51    48 

0   30   43   N.   A.  S 

<  30 

1836 

May      3     2    12      7 

0555 

0    26   40   N.   A.  (J 

S31 

1854 

May    14      8   50   4C 

0      4    19    45 

0   22    42   N.   A.  S 

5  32 

1872 

May    24   15  28   15 

0      3    26      3 

018      IN.   A.  <J 

S33 

1890 

June     4  22     8     0 

0      2    35      5 

0    13    34   N.   A.  S 

S  34 

1908 

-rune    15      4   38   23 

0      1    41    43 

0854   N.  A.  -^ 

S  35 

192* 

June    26    11    13     5 

0     0   47    38 

0     4    10  N.   A,  s 

\ 


Moons,  and  between  the  Sun's  mean  and  true  distances  from  the 
node,  the  Moon's  shadow  falls  even  with  the  Earth's  centre  two 
periods  sooner  in  this  table  than  in  the  first. 


Of  Eclipses. 


275 


**\»,  —  '  «                                                                                                                                                                                                                                .-' 

S  TABLE  IV.   The  true  Time  of  New  Moon,  with  the  Sun's  true  ^ 

S       Distance  from  the  Moon's  Ascending  Node,  and  the  Moon's  true  s 

*>       Latitude  at  each  periodical  Return  of  the  Sun's  E-clipse,  March  £ 

5       2lsf,  Old  Style,  A.  D.  1764,  from  its  falling  right  against  the  S 

J       Earth's  centre,  till  it  finally  leaves  the  Earth.                                  Jj 

^     T4  ^ 

True  Time  of 

Sun's  trueDist. 

Moon's  true  Lati-  S 

C     r^  rt 

>       0      £ 

2* 

->  $^ 

Mew  Moon 

from  the  Node. 

tude  South.       s, 

!i 

1.  *» 

0>     08 

r1"  o_ 

s 

Month.D.  H.  M.  S. 

s.       0      '      " 

0     '      "    South.  !j 

V     b  6 

i*44 

Juiy       6    17  50  35 

11    29    55    28 

0      0    24    S.     A.  £ 

S37 

1962 

July     18     0  31    38 

11    29      2    35 

0     5      2   S.    A.  S 

S  38 

198C 

July    28     7    18   53 

11    28    11    32 

0     9    29    S.     A.  Jj 

£  39 

1998 

Aug.     8    14    12   22 

11    27    26    41 

0    13   25   S.     A.S 

$40 

2016 

Aug.    18   21    14  53 

11    26   42    16, 

0    17    18   S.     A.  Jj 

541 

2034 

Aug.  30     4  25  45 

11    26      2      6 

0   20   48   S.     A.  S 

S42 

2052 

Sept.     9    11  45    17 

11    25    26   46 

0   23    53   S.     A.  ^ 

J  43 

2070 

:iept.  20    19    17  26 

11    24    55      4 

0   26   39   S.     A.  S 

^44 

2088 

Oct.       1      2   57     8 

11    24   27   43 

0   28   58    S.     A.  £ 

S45 

210r 

Oct.     12    10  47   39 

11    24     4    38 

031      2    S.     A.  S 

$46 

2124 

Oct.     22    18   37  40 

11    23   48   28 

0    32    26   S.    A.  Jj 

£  47 

2142 

Nov.      3      2   56    19 

11    23    35    11 

0    33    53    S.     A.  S 

S  48 

2160 

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S      By  the  true  motions  ol  the  Sun,  Moon,  and  nodes,  this  eclipse  S 

^  goes  off  the  Earth  four  periods  sooner  than  it  would  have  done  by  Jj 

S  mean  equable  motions.                                                                       '^ 

276  Of  Eclipses. 

From  "  To  illustrate  this  a  little  farther,  we  shall  exa- 

S^UT^'S  "  m"ie  somc  °f  th0  most  remarkable  circumstances 
disserta-   "  of  the  returns  of  the  eclipse,    which  happened 

edi^es,     "  July  14>    1748»   ab°Ut  n00n'      This  ecliPse»  after 

printed  'at "  traversing  the  voids  of  space  from  the  creation, 

Condon,     «  at  iast  began  to  enter  the  Terra  Australia  Incognita, 

C^VE,      "  about  88  years  after  the  Conquest,  which  was  the 

Sn  the  year"  last  of  King  STEPHEN'S  reign;  every  Chaldean* 

"  period  it  has  crept  more  northerly,  but  was  still 

"  invisible  in  Britain  before  the  year  1622;  when 

"  on  the  30th  of  April  it  began  to  touch  the  south 

**-  parts  of  England  about  2  in  the  afternoon  its  cen- 

"  tral  appearance  rising  in  the  American  South  Seas, 

"  and  traversing  Peru  and  the  Amazons^  country, 

*'  through  the  Atlantic  ocean  into  Africa,  and  setting 

<c  in  the  Ethiopian  continent,  not  far  from  the  begin- 

<{  ning  of  the  Red  Sea, 

"  Its  next  visible  period  was  after  three  Chaldean 
"  revolutions,  in  1676,  on  the  first  of  June,  rising 
c<  central  in  the  Atlantic  ocean,  passing  us  about  9 
"  in  the  morning,  with  four  f  digits  eclipsed  on  the 
"  under  limb ;  and  setting  in  the  gulph  of  Cochin- 
"  china,  in  the  East -Indies. 

"  It  being  now  near  the  solstice,  this  eclipse  was 
"  visible  the  very  next  return  in  1694,  in  the  even- 
"  ing ;  and  in  two  periods  more,  which  was  in  1730, 
"  on  the  4th  of  July,  was  seen  above  half  eclipsed 
*c  just  after  sun-rise,  and  observed  both  at  Ifittem- 
"  burg  in  Germany,  and  Pekin  in  China,  soon  af- 
"  ter  which  it  went  off. 

"  Eighteen  years  more  afforded  us  the  eclipse 
"  which  feli  on  the  14th  of  July,  1748. 

"  The  next  visible  return  will  happen  on  July  25, 
u  1766,  in  the  evening,  about  four  digits  eclipsed ; 

*  The  above  period  of  18  years,  11  days,  7  hours,  43  minutes,  20 

seconds,  was  found  out  by  the  Chaldeans,  and  by  them  called  Saros. 

t  A  digit  is  the  twelfth  part  of  the  diameter  of  the  Sun,  or  Moon 


Of  Eclipses.  277 

"•and  after  two  periods  more,  on  August  16th, 
"  1802,  early  in  the  morning,  about  five  digits,  the 
"  centre  coming  from  the  north  frozen  continent,  by 
"  the  capes  of  Norway,  through  Tartary,  China 
"  and  Japan ,  to  the  Ladrone  islands,  where  it  goes 
"  off. 

"  Again,  in  1820,  August  26,  betwixt  one  and 
"  two,  there  will  be  another  great  eclipse  at  London^ 
"  about  10  digits ,  but  happening  so  near  the  equi- 
"  nox,  the  centre  will  leave  every  part  of  Britain  to 
"  the  west,  and  enter  Germany  &  Embden,  passing 
"  by  Venice,  Naples,  Grand  Cairo ,  and  set  in  the 
"  gulf  of  Bassora  near  that  city. 

"  It  will  be  no  more  visible  till  1874,  when  five 
"  digits  will  be  obscured  (the  centre  being  now 
<c  about  to  leave  the  Earth)  on  September  28.  In 
"  1892,  the  Sun  will  go  down  eclipsed  at  London, 
"  and  again  in  1928  the  passage  of  the  centre  will  be 
"  in  the  expansion,  though  there  will  be  two  digits 
"  eclipsed  at  London,  October  the  31st  of  that  year; 
"  and  about  the  year  2090  the  whole  penumbra  will 
"  be  worn  off;  whence  no  more  returns  of  this  eclipse 
"  can  happen  till  after  a  revolution  of  ten  thousand 
"  years. 

"  From  these  remarks  on  the  entire  revolution  of 
"  this  eclipse,  we  may  gather  that  a  thousand  years 
"  more  or  less,  (for  there  are  some  irregularities  that 
"  may  protract  or  lengthen  this  period  100  years), 
"  complete  the  whole  terrestrial  phenomena  of  any 
"  single  eclipse:  and  since  20  periods  of  54  years 
u  each,  and  about  33  days,  comprehend  the  entire 
"  extent  of  their  revolution,  it  is  evident  that  the 
1 :  times  of  the  returns  will  pass  through  a  circuit  of 
;c  one  year  and  ten  months,  every  Chaldean  period 
"  being  ten  or  eleven  days  later,  and  of  the  equa- 
;c  ble  appearances  about  32  or  33  days.  Thus, 
"  though  this  eclipse  happens  about  the  middle  of 
"  July,  no  other  subsequent  eclipse  of  this  period 
il  will  return  to  the  middle  of  the  same  month  again ; 


Of  Eclipses. 

"  but  wear,  constantly  each  period  10  or  11  days 
"  forward  ;  and  at  last  appear  in  winter,  but  then  it 
<l  begins  to  cease  from  affecting  us. 

"  Another  conclusion  from  this  revolution  may 
* '  be  drawn,  that  there  will  seldom  be  any  more  than 
"  two  great  eclipses  of  the  Sun  in  the  interval  of 
"  this  period,  and  these  follow  sometimes  next  return, 
4C  and  often  at  greater  distances.  That  of  1715  re- 
*c  turned  again  in  1733  very  great;  but  this  present 
"  eclipse  will  not  be  great  till  the  arrival  of  1820, 
"  which  is  a  revolution  of  four  Chaldean  periods ; 
"  so  that  the  irregularities  of  their  circuits  must 
"  undergo  new  computations  to  assign  them  ex- 
"actly. 

"  Nor  do  all  eclipses  come  in  at  the  south  pole: 
tc  that  depends  altogether  on  the  position  of  the  lu- 
"  nar  nodes,  which  will  bring  in  as  many  from  the 
"  expansum  one  way  as  the  other :  and  such  eclips- 
"  es  will  wear  more  southerly  by  degrees;  contrary 
"  to  what  happens  in  the  present  case. 
"  The  eclipse,  for  example,  of  1736,  in  Septem- 
"  6er,  had  its  centre  in  the  expansum,  and  set  about 
"  the  middle  of  its  obscurity  in  Britain  ;  it  will  wear 
"  in  at  the  north  pole,  and  in  the  year  2600,  or 
"  thereabout,  go  off  in  the  expansum  on  the  south 
"  side  of  the  Earth. 

"  The  eclipses  therefore  which  happened  about 
"  the  creation  are  little  more  than  half  way  yet  of 
"  their  ethereal  circuit ;  and  will  be  4000  years  be- 
"  fore  they  enter  the  Earth  any  more.  This  grand 
"  revolution  seems  to  have  been  entirely  unknown 
"  to  the  ancients. 

prehsentta-      322'  " It:  is  particularly  to  be  noted,  that  eclipses 

bies  agree  "  which  have  happened  many  centuries  ago,  will  not 

ancient**    *  *  ^e  ^ounc^  by  our  present  tables  to  agree  exactly  with 

observa-    ' '  ancient  observations,  by  reason  of  the  great  anoma- 

tion.         «t  j-es  mtne  lunar  motions ;  which  appears  an  incon- 

"  testable  demonstration  of  the  non-eternity  of  the 

"  universe.     For  it  seems  confirmed  by  undent- 


Of  Eclipses.  279 

"  able  proofs,  that  tbe  Moon  now  finishes  her  period 
"  in  less  time  than  formerly,  and  will  continue  by 
"  the  centripetal  law  to  approach  nearer  and  nearer 
"  the  Earth,  and  to  go  sooner  and  sooner  round  it : 
"  nor  will  the  centrifugal  power  be  sufficient  to  com- 
"  pensate  the  different  gravitations  of  such  an  as- 
"  semblage  of  bodies  as  constitute  the  solar  system, 
"  which  would  come  to  ruin  of  itself,  without  some 
"  new  regulation  and  adjustment  of  their  original 
"  motions*. 

323.  "  We  are  credibly  informed  from  the  testi- THALES'S 
"  mony  of  the  ancients,  that  there  was  a  total  eclipse  ecllPse- 

*  There  are  two  ancient  eclipses  of  the  Moon,  recorded  by  Pto- 
lemy from  Hipparchus,  which  afford  an  undeniable  proof  of  the 
Moon's  acceleration.  The  first  of  these  was  observed  at  Babylon^ 
December  the  22d,  in  the  year  before  CHRIST  383 :  when  the  Moon 
began  to  be  eclipsed  about  half  an  hour  before  the  Sun  rose,  and  the 
eclipse  was  not  over  before  the  Moon  set :  but  by  most  of  our  astro- 
nomical tables  the  Moon  was  set  at  Babylon  half  an  hour  before  the 
eclipse  began  ;  in  which  case,  there  could  have  been  no  possibility  of 
observing  it.  The  second  eclipse  was  observed  at  Alexandria,  Sep.- 
tember  the  22d,  the  year  before  CHRIST  201;  where  the  Moon  rose 
so  much  eclipsed,  that  the  eclipse  must  have  begun  about  half  an 
hour  before  she  rose  ;  whereas,  by  most  of  our  tables,  the  beginning 
of  this  eclipse  was  not  till  about  ten  minutes  after  the  Moon  rose  at 
Alexandria.  Had  these  eclipses  begun  and  ended  while  the  Sun  was 
below  the  horizon,  we  might  have  imagined,  that  as  the  ancients  had 
no  certain  way  of  measuring  time,  they  might  have  been  so  far  mis- 
taken in  the  hours,  that  we  could  not  have  laid  any  stress  on  the  ac- 
counts given  by  them,  But,  as  in  the  first  eclipse  the  Moon  was  set, 
and  consequently  the  Sun  was  risen,  before  it  was  over ;  and  in  the 
second  eclipse  the  Sun  was  set  and  the  Moon  not  risen,  till  sometime 
after  it  began ;  these  are  such  circumstances  as  the  observers  could 
not  possibly  be  mistaken  in.  Mr.  Struyk,  in  the  following  catalogue, 
notwithstanding  the  express  words  of  Ptolemy,  puts  down  these 
two  eclipses  as  observed  at  Athens ;  where  they  might  have  been 
seen  as  above,  without  any  acceleration  of  the  Moon's  motion: 
Athens  being  20  degrees  west  of  Babylon^  and  7  degrees  west  of 
Alexandria. 

Nn 


280  Of  Eclipses. 

"  of  the  Sun  predicted  by  THALES  to  happen  in  the 
"  fourth  year  of  the  48th'*  Olympiad,  either  at  Sar- 
"  dis  or  Miletus  in  Asia,  where  THALES  then  re- 
"  sided.  That  year  corresponds  to  the  585th  year 
*'  before  Christ;  when  accordingly  there  happened 
"  a  very  signal  eclipse  of  the  Sun,  on  the  28th  of 
"  Mat/,  answering  to  the  present  10th  of  that  monthf, 
"  central  through  North  America,  the  south  parts  of 

*  Each  Olympiad  began  at  the  time  of  full  Moon  next  after 
the  summer- solstice,  and  lasted  four  years,  which  were  of  une- 
qual lengths,  because  the  time  of  full  M<  on  differs  11  days  every 
year :  so  that  they  might  sometimes  begin  on  the  next  day  after  the 
solstice,  and  at  other  times  not  till  four  weeks  after  it.  The  first 
Olympiad  began  in  the  year  of  the  Julian  period  5938,  which  was 
776  years  before  the  first  year  of  CHRIST,  or  775  before  the  year  of 
his  birth ;  and  the  hist  Olympiad,  which  was  the  293d,  began  A*  D. 
S93.  At  the  expiration  of  each  Olympiad,  the  Olympic  Games  were 
celebrated  in  the  Elcan  fields,  near  the  river  Alfiheus  in  the  Pclo/ion- 
neaus  (now  Marco)  in  honour  of  JUPITER  OLYMPUS.  See  STRAU- 
CHIUS'S  Breviarium  Chronologicum,  p.  247 — 251. 

t  The  reader  may  probably  find  it  difficult  to  understand  why  ATr. 
SMITH  should  reckon  this  eclipse  to  have  been  in  the  4th  year  of  the 
48th  Olympiad,  as  it  was  only  in  the  end  of  the  third  year :  and  al- 
so why  the  28th  of  May,  in  the  535th  year  before  CHRIST,  should 
answer  to  the  present  10th  of  that  month.  But  we  hope  the  follow- 
ing explanation  will  remove  these  difficulties. 

The  month  of  May  (when  the  Sun  was  eclipsed)  in  the  585th  year 
before  the  first  year  of  CHRIST,  which  was  a  leap-year,  fell  in  the 
latter  end  of  the  third  year  of  the  48th  Olympiad;  and  the  fourth 
year  of  that  Olympiad beg-in  at  the  summer-solstice  following:  but 
perhaps  Mr.  SMITH  begins  the  year  of  the  Olympiad  from  January, 
in  order  to  make  them  correspond  more  readily  \vith  Julian  \ears; 
and  so  reckons  the  month  of  May,  when  the  eclipse  happened,  to  be 
in  the  fourth  year  of  that  Olympiad. 

Tiie  place  or  longitude  of  the  Sun  at  that  time  was  b»  29°  43'  17", 
to  which  same  place  the  Son  returned  (after  2300  years,)  -viz,  A.  D. 
1716,  on  May  S<*  $*>  O  after  noon:  so  that,  with  respect  to  the  Sun's 
place,  the  9th  of  May,  1716,  answers  to  the  28th  of  May  in  the  585th 
year  before  the  first  year  cf  CHRIST  ;  that  is,  the  Sun  had  the  same 
longitude  on  both  those  days.  » 


Of  Eclipses.  281 

"  France,  Italy,  £cc.  as  far  as  Athens,  or  the  isles 
**  in  theJEgean  Sea;  which  is  the  farthest  that  even 
"  the  Caroline  tables  carry  it;  and  consequently 
"  make  jt  inv  bible  to  any  part  of  Asia,  i;i  the  total 
"  character;  though  I  have  good  reasons  to  believe 
"  that  it  extended  to  Babylon,  and  went  down  cen- 
"  trai  over  that  city.  We  are  not  however  to  ima- 
"  gine,  that  it  was  set  before  it  passed  Sardts  and  the 
41  Asiatic  towns,  where  the  predictor  lived;  because 
"  an  invisible  eclipse  could  have  been  of  no  service 
<{  to  demonstrate  his  ability  in  asironomicrj  sciences 
"  to  his  countrymen,  as  it  could  give  no  proof  of  its 
"  reality. 

324.  "For  a  further  illustration,  THUCYDIDES  THUCY- 
"  relates,  that  a  solar  eclipse  happened  on.  a  sum- 
"  mer's  day  in  the  afternoon,  in  the  first  year  of  the 
*'  Peloponneslan  war,  so  great  that  the  stars  appcar- 
u  ed.  RIIODIUS  was  victor  in  the  Olympic  games 
u  the  fourth  year  of  the  said  war,  being  also  the 
"  fourth  of  the  87th  Olympiad,  on  the  428th  year 
tl  before  CHRIST.  So  that  the  eclipse  must  have 
"  happened  in  the  431st  year  before  CHRIST:  and 
"  by  computation  it  appears,  that  on  the  3d  of  An- 
"  gust  there  was  a  signal  eclipse  which  would  have 
"  passed  over  A t hens,  central  about  G  in  the  even- 
"  ing,  but  which  our  present  tables  bring  no  farther 
u  than  the  ancient  Syrtes  on  the  African  coast,  above 
u  400  miles  from  Athens ;  which  suffering  in  that 
u  case  but  9  digits,  could  by  no  means  exhibit  the 
"  remarkable  darkness  recited  by  this  historian  ;  the 
"  centre  therefore  seems  to  have  passed  Athens  about 
u  6  in  the  evening,  and  probably  might  go  down 
"  about  Jerusalem,  or  near  it,  contrary  to  the  con- 
"  struction  of  the  present  tables.  I  have  only  ob- 
<c  viated  these  things  by  way  of  caution  to  Nie  pre- 
E*  sent  astronomers,  in  re-computing  ancient  eclip- 
"  ses ;  and  refer  them  to  examine  the  eclipse  of  Ni- 
'i  cias,  so  fatal  to  the  Athenian  fleet*.;  that  which 

*  Before  CHRIST  413,  dugttst  ?r. 


282  Of  Eclipses. 

11  overthrew  the  Macedonian  army*,  &V."     So  far 
Mr.  SMITH. 

The  num.  325.  In  any  year,  the  number  of  eclipses  of  both 
ecli°ses  ^uminaries  cannot  be  less  than  two,  nor  more  than 
seyen ;  the  most  usual  number  is  four,  and  ii  is  very 
rare  to  have  more  than  six.  For  the  Sun  passes  by 
both  the  nodes  but  once  a  year,  unless  he  passes  by 
one  of  them  in  the  beginning  of  the  year  ;  and  when 
he  does,  he  will  pass  by  the  same  node  again  a  little  be- 
fore the  year  be  finished ;  because  as  these  points 
move  19-y  degrees  backward  every  year,  the  Sun 
will  corne  to  either  of  them  173  days  after  the  other, 
§  319.  And  when  either  node  is  within  17  degrees 
of  the  Sun  at  the  time  of  new  Moon,  the  Sun  will 
be  eclipsed.  At  the  subsequent  opposition,  the 
Moon  will  be  eclipsed  in  the  other  node ;  and  come 
round  to  the  next  conjunction  again  ere  the  former 
node  be  17  degrees  past  the  Sun,  and  will  therefore 
eclipse  him  again.  When  three  eclipses  fall  about 
either  node,  the  like  number  generally  falls  about 
the  opposite ;  as  the  Sun  comes  to  it  in  173  days  af- 
terward ;  and  six  lunations  contain  but  four  days 
more.  Thus  there  may  be  two  eclipses  of  the  Sun 
and  one  of  the  Moon  about  each  of  her  nodes.  But 
when  the  Moon  changes  in  either  of  the  nodes,  she 
cannot  be  near  enough  the  other  node  at  the  next  full 
to  be  eclipsed;  and  in  six  lunar  months  afterward 
she  will  change  near  the  other  node :  in  these  cases 
there  can  be  but  two  eclipses  in  a  year,  and  they  will 
be  both  of  the  Sun. 

326.  A  longer  period  than  the  above  mentioned, 
§  320,  for  comparing  and  examining  eclipses  which 
happened  at  long  intervals  of  time,  is  557  years  21 
days  18  hours  30  minutes  11  seconds,  in  which 
time  there  are  6890  mean  lunations :  and  the  Sun 
and  node  meet  again  so  nearly  as  to  be  but  11  se- 
conds distant ;  but  then  it  is  not  the  same  eclipse  that 
returns,  as  in  the  shorter  period  above-mentioned. 

*  Before  CHRIST  168,  June  21. 


Of  Eclipses.  233 

327.     We  shall  subjoin  a  catalogue  of  eclipses 
recorded  in  history,  from  721  years  before  CHRIST 
to  A.  D.  1485  ;  of  computed  eclipses  from  1485  to 
1700:  and  of  all  the  eclipses  visible  in  Euro/whom 
1700  to   18CO.     From  the  beginning  of  the  cata- 
logue to  A.  /).  1485,  the  eclipses  are  taken  from 
STRUYK'S  Introduction    to    Universal  Geography,  An  ac- 
as  that  indefatigable  author  has,  with  much  labour,  ^"'^fw, 
collected  them  from   Ptolemy,    Timcydidcs,  Pin-  ing-  cata- 
ta?'c/i9  Calvisius,  Xenophon,  Jjiodorus  Siculus,  Jus-  lo£ue  of 
tin,  Polybius,  Titus  Livius,  Cicero,  Lucanus,  The-* 
ophanes*  Dion,  Cassias,  and  many  others.     From 
1485  to  1700  the  eclipses  are  taken  from  Ricciolus's 
Almagest:  and  from  1700  to  1800  from  L?Art  dc 
verifier  les  Dates.     Those  from  Struyk  have  all  the 
places  mentioned  where  they  were  observed :  Those 
from  the  French  authors,  viz.  the  religious  Benedict 
tines  of  the  congregation  of  St.  Maur,  are  fitted  to 
the  meridian  of  Paris:  And  concerning  those  from 
Ricciolus,  that  author  gives  the  following  account : 

"  Because  it  is  of  great  use  for  fixing  the  cycles 
or  revolutions  of  eclipses,  to  have  at  hand,  without 
the  trouble  of  calculation,  a  list  of  successive  eclip- 
ses for  many  years,  computed  by  authors  of  ephe- 
mcrides,  although  from  tables  not  perfect  in  all  re- 
spects, I  shall,  for  the  benefit  of  astronomers,  give  a 
summary  collection  of  such.  The  authors  I  extract 
from  are  :  an  anonymous  one  w  ho  published  ephe- 
meridesfrom  1484  to  1506  inclusive:  Jacobus  Ptlau- 
men  and  Jo.  St&flerinus,  to  the  meridian  of  Vim, 
from  1507  to  1534:  Lucas  Gauricus,  to  the  latitude 
of  45  degrees,  from  1534  to  1551 :  Peter  Appian, 
to  the  meridian  of  Lei/sing,  from  1538  to  1578  :  Jo. 
Sttfflerus,  to  the  meridian  of  Tubing,  from  1543  to 
1554 :  Petrus  Pitatus,  to  the  meridian  of  Venice, 
from  1554  to  1556:  Georgius  Joachimus  Rheticus, 
for  the-y^ar  1551 :  Nicholas  Simus,lo  the  meridian 
of  Bologna,  from  1552  to  1568  :  M. ichael  Mastlin, 
to  the  meridian  of  Tubing,  from  1557  to  1590:  Jo. 


Stadius,  to  the  meridian  of  Antwerp,  from  1554  to 
1574  :  Jo.  Antoninus  Maginus^  to  the  meridian  of  Ve- 
nice^ from  1581  to  1630  :  David  Origan  to  the  meri- 
dian of  Franckfort  on  the  Oder,  from  1595  to  1664 : 
Andrew  Argol,\a  the  meridian  of  Home,  from  1630  to 
1700  :  Franciscus  Montchrunus,  to  the  meridian  of 
Bologna,  trom  1461  to  1660:  Among  which,  Sta- 
dius,  Mtfstlin,and  Maginus,  used  the  Prutenic  tables; 
Origan  the  Prutenic  and  Tychonic;  Montebrunus\hz 
Lansbergian,  as  likewise  those  of  Durat.  Almost 
all  the  rest  the  Alphonstne. 

"  But  that  the  places  may  readily  be  known  for 
which  these  eclipses  were  computed,  and  from  what 
tables,  consult  the  following  list,  in  which  the  years 
inclusive  are  also  set  down  : 

From         To 

1485  1506  The  place  and  author  unknown. 

1507  1553  Ulm  in  Suabia,  from  the  Alphonsine. 

1554  1576  Antwerp,  from  the  Prutenic. 

1577  1585   Tubing,  from  the  Prutenic. 

1586  1594  Venice,  from  the  Prutenic.          \Jenic. 

1595  1600  Franckfort  on  the  Oder,  from  the  Pru- 

1601  1640  Franc/cfortQnthcOderJromthtTychonic 

1641  1660  Bologna,  from  the  Lansbcrgian* 

1661  1700  Rome,  from  the  Tychonic" 

So  far  RICCIOLUS. 

JY.  B.  The  eclipses  marked  with  an  asterisk  are 
not  in  Rice  10 LUS'S  catalogue,  but  are  supplied  from 
L'Art  de  verifier  les  Dates. 

From  the  beginning  of  the  catalogue  to  A.D.  1700, 
the  time  is  reckoned  from  the  noon  of  the  day  men- 
tioned to  the  noon  of  the  following  day :  but  from 
1700  to  1800  the  time  is  set  down  according  to  our 
common  way  of  reckoning.  Those  markedhjPfto 
and  Canton  are  eclipses  from  the  Chinese  chronology 
according  to  STRUYK  ;  and  throughout  the  table  this 
mark  ©  signifies  Suny  and  3  Moon. 


Of  Eclipses. 


285 


STRUYK's  CATALOGUE  OF  ECLIPSES. 


JJff. 

jLcii;>s  /a  ul   Uie  iuu 

4.   and  D. 

JHidiilu 

Digits 

Chr. 

and  Moon  seen  ut 

H.  M 

eclipsed. 

721 

Babylon 

3 

March      1910     34 

Total 

720 

Babylon 

5 

March       8. 

11     56 

1       5 

720 

Babylon 

^) 

icpt.          1 

10     18 

5       4 

621 

Babylon 

D 

Apr.        21 

18     2; 

2     36 

523 

Babylon 

D 

July         16 

13     47 

7     24 

502 

Babylon 

3 

Nov.         19 

12     21 

1     52 

491 

Babylon 

5 

April       25 

12     1? 

1     44 

431 

Athens 

© 

Aug.          3 

6     35 

11       0 

425 

Athens 

"2 

Oct.            9 

6     45 

Total 

424 

Athens 

March     20 

20    ir 

9       0 

413 

Athens 

if 

Aug.        27 

10     lo 

Total 

406 

Athens 

3> 

Apr.         15 

8     50 

Total 

404 

Athens 

(v) 

Sept.          2 

21     12 

8     40 

403 

Pekin 

(v) 

Aug.        28 

5     53 

10    40 

394 

Gnide 

© 

Aug.        13 

22     17 

11       0 

383 

Athens 

J) 

Dec.        2i 

19       o 

2       1 

382 

Athens 

D 

June         18 

rt     54 

6     15 

382 

Athens 

~j) 

Dec.        12 

10     21 

Total 

364 

1'hebes 

p 

July          K 

23     51 

6     10 

357 

Syracuse 

© 

Feb.         28 

22'    — 

3     33 

357 

Zant 

D 

Aug.        29 

7     2° 

4    21 

340 

Zant 

© 

Sept.        14 

18    - 

9       0 

331 

Arbela 

j 

Sept.        20 

20       i 

Total 

310 
219 

Sicily  Island 
Mysia 

0 

Aug.        14 
March     19 

-20       5 
14       5 

10     22 
Total 

218 

Pergamos 

2 

Sept.          1 

rising 

Total 

217 

Sardinia 

(v) 

Feb.         11 

1     57 

9       6 

203 

Frusini 

S 

May           6 

2     5? 

5    40 

202 

Cumis 

(B 

Oct.          18 

22     24 

1       0 

201 

Athens 

D 

Sept.        22 

7     14 

.  8     58 

200 

Athens 

D 

March     19 

13       < 

Total 

200 

Athens 

3 

Sept.        11 

14     4^ 

Total 

198 

H.OTOC 

f»?\ 

Aue*           9 

9 

190 

Rome 
Rome 

1 

JT-ug.               y 

March      15 
July          16 

18     ~ 
20     St. 

11       0 

10    43 

174 

Athens 

D 

April       30 

14     3> 

7      1 

168 

Macedonia 

J) 

June         2] 

8       2 

Total 

141 

Rhodes 

^) 

Jan.          27 

10       I 

3     26 

104 

Rome 

© 

July         IS 

22       0 

11     52 

'    63 

Rome 

j) 

Oct.         27 

6     2. 

Total 

60 

Gibraltar 

§i 

March     16 

settiiu 

Central 

54 

Canton 

May           9 

3     4i 

Total 

51 

Rome 

March       7 

2     1^ 

9       0 

48 

Rome 

D 

Jan.          18 

10       ( 

Total 

45 

ilome 

J 

Nov.          6 

4     - 

Total 

36 

Rome 

© 

May         19 

3     5: 

6    47_ 

Of  Eclipses. 

STRUYK's  CATALOGUE  OF  ECLIPSES. 


Wei: 

Chr. 

eclipse*  oi   tlie  bun 
and  Moon  seen  at 

M.  and  D. 

Middle 
H.  M 

iJlglt.S      * 

eclipsed. 

31 

Rome 

*-y\ 

Aug.        20 

setting 

Gr.  Eel. 

29 

Canton 

£v) 

Jan.           5 

4       2 

11       0 

28 

Pekin 

© 

June         18 

23    48 

Total 

26 

Canton 

© 

Oct.         23 

4     16 

11     15 

24 

Pekin 

3? 

\pril         7 

4     11 

2       0 

16 

Pekin 

(v) 

Nov.           1 

5     13 

2       8 

2 

Canton 

® 

Feb.           1 

20       8 

11     42 

Aft. 

Chr. 

1 

Pekin 

June         10 

1     10 

U     43 

SjRome 

March     28 

4     15 

4    45 

14  Pannonia 

J 

Sept.        26 

17     15 

Total 

27jCanton 

July         22 

8     56 

Total 

SOCanton 

© 

Nov.         ir, 

19     20 

10     30 

40:pekin 

(v) 

-\pril        30 

5     50 

7     ot 

45  Rome 

(y) 

July         31 

.2       1 

5     17 

46  Pekin 

© 

July         21 

.22    .55 

2     10 

46  Rome 

3 

Dec.        .'U 

9   5: 

Total 

49  Pekin 

(v) 

lay         2i> 

7     16 

10       8 

53;  Canton 

© 

viarch       8 

20     4C- 

11       6 

55|  Pekin 

(v) 

July          12 

•1    5u 

6     40 

56i  Canton 

/v} 

Ice.        2o 

0     28 

9     20 

59|R')me 

© 

\pril       SO 

3       8 

10    38 

60  Canton 

© 

Oct.          13 

3     31 

10     SO 

65  Canton 

© 

Dec.         15 

21     50 

lO     23 

691  Rome 

J) 

Oct.          18 

10     43 

10    49 

70  Canton 
71  Rome 

© 

3) 

Sept.        2i 
March       4 

31     13 

8     32 

8    26 
6       (j 

95jEphesus 
125  Alexandria 

f 

Mav         21 
April          5 

1    .  0 
1     44 

9     16 

133 

Alex  Adda 

D 

VTay           6 

11      44 

Total 

134 

Alexandria 

D 

Oct.          2C 

LI 

!0     19 

136 

Alexandria 

D 

\Iarch        5 

1  5     56 

5     17 

237 

Bologna 

april        12 



Total 

238 

Rome 

Vpril          1 

•20     20 

8     45 

290 

Carthage 

May          15 

3     20 

i  1     20 

304 

Rome 

3 

Aug.         S3 

9     36 

fotal 

316 

Constantinople 

© 

Dec.         30 

19     53 

2     18 

334 

Toledo 

© 

July          17 

atnoo- 

Central 

348 

Constantinople 

© 

Oct.            £ 

19     2^ 

3       f; 

360 

Ispahan 

© 

Aug.        27 

;8      ( 

Central 

364 

Alexandria 

5 

tfov.         25 

!5     24 

l'oU| 

401 

Rome 

Tj 

[nne         1" 

t'otal 

'401 

Rome 

M 

3 

Dec.           6 

32      1-v 

<'otal 

402 

ilome 

3 

June           1 

8     4., 

10       2 

Of  Eclipses. 
STRUYK's  CATALOGUE  OF  ECLIPSES* 


387 


Aft. 
Chr, 

Eclipses  of  the  Sun 
and  Moon  seen  at 

M.andD. 

Middle 
H.    M 

Digits    "S 
eclipsed.  J» 

402 

Rome 

Nov.    10 

20    33 

10        30  S 

447 

Compostello 

Dec.    23 

0     46 

1        —  S 

451 

Compostello 

April     1 

16     34 

19        52  h 

451 

Compostello 

3 

Sept.    26 

6    30 

0          2? 

458 

Chares 

© 

May    27 

23     16 

18        53  S 

462 

Compostello 

D 

March  1 

13      2 

11         11  \ 

464 

C  haves 

^ 

July      19 

19       1 

10         15  ? 

484 

Constantinople 

3 

Jan.      13 

19    53 

10          0? 

486 

Constantinople 

o 

May     19 

1     10 

5         15  S 

497 

Constantinople 

5 

April    18 

6      5 

17        57  {> 

512 

Constantinople 

\-) 

June     25 

23      8 

1         50  ? 

538 

England 

} 

Feb.     14 

19    — 

8         23  ? 

540 

London 

v) 

June     19 

20     15 

8        —  S 

577 

Tours 

5 

Dec.    10 

17    28 

6        46  > 

581 

Paris 

D 

April     4 

^3     33 

6        42  w 

582 

Paris 

D 

Sept.    17 

12    41 

Total     S 

590 

Paris 

D 

Oct.     18 

6    30 

9        25  S 

592 

Constantinople 

Marchl8 

22       6 

10          0  < 

603 

Paris 

© 

Aug.     12 

3       3 

11        20  S 

622 

Constantinople 

D 

Feb.       1 

11     28 

Total     S 

644 

Paris 

© 

Nov.      5 

0    30 

9        53  Ij 

680 

Paris 

D 

June     17 

12     30 

Total     c 

683 

Paris 

D 

April    16 

11     30 

Total     S 

693 

Constantinople 

© 

Oct.       4 

23    54 

11        54  J» 

736 

Constantinople 

Jan.      13 

7    — 

Total     J 

718 

Constantinople 

June       3 

1     15 

Total     C 

733 

England 

Aug.    13 

20     — 

11          IS 

734 

England 

D 

Jan.     23 

14    — 

Total     S 

752 

England 

J) 

July      30 

13     — 

Total     ? 

753 

England 

© 

June       8 

2<J     — 

10        35  S 

753 

England 

D 

Jan.      23 

13    — 

Total     S 

760 

England 

© 

Aug.     15 

4     — 

8        15  £ 

760 

London 

D 

Aug.    30 

5     50 

10         40  c 

764 

England 

© 

June       4 

at  noon 

7         15  S 

770 

London 

^) 

Ftb.     14 

7     12 

Total    S 

774 

Rome 

^) 

Nov.     22 

14     37 

11        58  > 

784 

London 

j) 

Nov.       1 

14       ^ 

Total     C 

787 
796 

Constantinople 
Constantinople 

© 

D 

Sept.    14 
March27 

20    43 
16    22 

9        47  S 
Total     S 

800 

Rome 

D 

Jan.      15 

9      0 

10     17  J; 

807 
807 

Angoulesme 
Paris 

© 
D 

Ffeb.     10 
Feb.     25 

21     24 
13     43 

9        42? 
Total     S 

807 

Paris 

D 

Aug.    21 

10     20 

Total    £ 

809 

Paris 

© 

July       15 

21     33 

8          8? 

809 

Paris 

Dec.     25 

8    — 

Total     s 

810 
f^*r 

Paris 
s~*r-rj*s*^j*s>fjrsj 

j> 
•VT.J 

June     20 
ns*s*j*j-*r 

8    — 
^s**r*r 

Total     S 
.r-r,/--r»r<\)* 

Go 


Of  Eclipses. 
STRUYK's  CATALOGUE  OF  ECLIPSES. 


S    Aft.  I 
S    Chr. 

Eclipses  of  the  Sun 
and  Moon  seen  at 

1 

Viand  D. 

Middle 

i.  M. 

Digits     S 
eclipsed    P 

s      810  Paris 

3>  Nov.    30 

0     12 

Total     S 

S      810 

'aris 

D  Dec.     14 

8    — 

Total    S 

J      812 

Constantinople 

R 

May     14 

2     13 

9        —  J 

2      813 

Cappadocia 

May      3 

7      5 

10        35  ^ 

S      81? 

Paris 

5 

Feb.       5 

5    42 

Total     S 

S      818 

Paris 

p 

July        6 

18     — 

6        35  £ 

£      820 

Paris 

Hi 

Nov.    23 

6    26 

Total     L 

^'     824 

Paris 

D 

March  IB 

7     55 

Total     s 

S      828 

Paris 

D 

June     30 

5     — 

Total     S 

S      828 

Paris 

D 

Dec.    24 

13     45 

Total    { 

831 

Paris 

D 

April   30 

6     19 

11         8? 

S      831 

Paris 

May     15 

23    — 

4        24  S 

7 

S      831 

Paris 

? 

Oct.     24 

11     18 

Total     S 

V     832|  Paris 

April   18 

9       0 

Total    2 

J      84  Oi  Paris 

*,) 

May      4 

23     22 

9        20  S 

^      841j  Paris 
S      842  Paris 

© 

D 

Oct.      17 
March  29 

18    5fc 
14     38 

5        24  S 
Total    £ 

S      843]  Paris 

D 

March  19 

7      1 

Total     5 

<      861 

Paris 

D 

March  29 

15      7 

Total    S 

S      878 

Paris 

D 

Oct.      14 

16    — 

Total    £ 

S      878 

Paris 

Oct.     29 

1     — 

11        14  J 

i      883 

Arracta 

5 

July      23 

7     44 

11        —  ? 

S      889 

Constantinople 

/77" 

April     o 

17    52 

£       23  S 

S      891 

Constantinople 

S 

Aug.      7 

23    48 

10        30  J 

>      501 

Arracta 

J 

Aug.      2 

15       7 

Total     s 

5      904 

London 

5 

May     3 

11     47 

Total     S 

S      904 

London 

D 

Nov.    2 

9       C 

Total     J 

S      912 

London 

D 

Jan. 

15     11 

Total     c 

£      926 

Paris 

March  31 

15     17 

Total     S 

5      934 

Paris 

© 

April    16 

4     30 

11        36  J 

S      939 

Paris 

July      18 

19     45 

10          7  £ 

S      955 

Paris 

T) 

Sept.     4 

11     18 

Total     s 

J      961 

Rh  ernes 

S 

May     16 

20     13 

9        18  S 

<      970 

Constantinople- 

May      7 

18     Sfr 

11        22  £ 

S      976 

London 

5  July    to 

15       7 

Total     t 

V      985 

Messina 

© 

July      2i 

3    52 

4        10  S 

^      98? 

Constantinople 

P"- 

May     2S 

6    54 

8        40  S 

^      99C 

Fulda 

5 

April    li 

10     22 

9          5  > 

S      99C 

Fulda 

Oct.       6 

15       4 

1        10  <J 

*»      99C 

Constantinople 

i 

Oct.     21 

0     45 

10          5  S 

{      995 

Augsburga 

3) 

July       14 

11     27 

Total    £ 

c   iocs 

Ferrara 

3 

Oct.       € 

11     56 

Total     J 

S     101C 

Messina 

j) 

March  1£ 

5     41 

9        12? 

S     1016 

N  5  meg-uen 

Nov.     1C 

16     39 

Total    j 

5    1017 

Niiriegr.en 

K 

Oct.     22 

2      8 

6     rs 

s   io^c 

Cologne 

5 

Sept.      411     3S 

Total     s 

Of  Eclipses. 
STRUYK's  CATALOGUE  OF  ECLIPSES. 


589 


* 


my* 


S  Aft.] 
S  Ch'-. 

Eclipses  of  the  Sun 
and  Moon  seen  at 

M.amlD. 

Middle 

H.    M. 

Digits    'S 
eclipsed.  S 

S  1023 

London 

© 

Jan.      23 

2:3     29 

11         —  S 

S  1030 

Rome 

'^ 

Feb.     20 

11     43 

Total     S 

J  1031 

Paris 

J) 

Feb.       9 

11     51 

Total     S 

S  1033 

Paris 

D 

Dec.       8 

11     11 

9         17  £ 

S  1034 

Milan 

D 

June      4 

9       8 

Total      s 

J  1037 

Paris 

Apr.     17 

20     45 

10         45  S 

J  1039 

Auxerre 

/v"j 

Aug.    21 

23    40 

11        5J; 

S  104'J 

Elome 

D 

Jan.        8 

16    39 

Total      t 

S  1044 

Aaxerre 

j) 

Nov.       7 

16     12 

10           IS 

J  1044 

Cluny 

© 

Nov.     21 

22     12 

11         -S 

2  1056 

Nurembui'g 

April     2 

12      9 

Total      £ 

S  1063 

Rome 

D 

Nov.       8 

12     16 

Total      ^ 

S  1074 

Augsburgh 
Constantinople 

D 

D 

Oct.        7 
Nov.     29 

10     13 
11     12 

Total      S 
9         36^ 

S  1082 

Condon 

May     14 

10    32 

10           2  ? 

S  1086 

Constantinople 

© 

Feb.      16 

4      .7 

Total     s 

S  1089 

Naples 

j) 

June     25 

6       6 

Total     S 

J  1093 

Augsburgh 

© 

Sept.    22 

22     35 

10     12  r> 

S  1096 

Gembluors 

D 

Feb.      10 

16       4 

Total     ^ 

S  1096 

Augsburgh 

D 

Aug.      6 

8     21 

Total     S 

J  1098 
c  1099 

Augsburgh 
Naples 

© 

D 

Dec.     25 
Nov.     30 

1     25 
4     58 

0        12  S 
T-otal     J 

S  1103 

Rome 

D 

Sept.    17 

10     18 

Total     t 

S  1106 

irfurd 

D 

July      17 

11     28 

11         54  S 

J  1107 

Naples 

D 

Jan.      10 

13     16 

Total     S 

J  1109 

Erfurd 

© 

May    31 

1     30 

10        20  J 

s  mo 

Condon 

3 

May       5 

10     51 

Total     <J 

S  1113 

ferusalem 

March  18 

19       0 

9        12  S 

?  1114 

l.ondon 

5 

Aug.    17 

15       5 

Total      S 

S  1117 

Triers 

5 

June     15 

13     26 

Total      J 

S  1117 

Triers 

D 

Dec.    10 

12     51 

Total      t 

J  1110 

Naples 

D 

Nov.     20 

15    46 

4        US 

<  1121 

Triers 

D 

Sept.    27 

16     47 

Total     S 

S  H22 

Prague 

D 

March  24 

11     20 

3         49? 

S  1124 

irfurd 

Feb.        1 

6     43 

8         39  S 

J*  1124 

London 

© 

Aug.    10 

23     29 

9         58  S 

C  1132 

irf'urd 

D 

March   3 

8     14 

Total      ? 

S  1133 

Prague 

D 

Feb.     20 

16     41 

3         23  <J 

J  1135 

London 

D 

Dec.     22 

20     11 

Total     S 

J  1142 

Rome 

D 

Feb.      1  1 

14     17 

8        30  S 

S  H43 

Rome 

Feb.        1 

6    36 

Total     h 

S  1147 

Auranches 

© 

Oct.     25 

22    38 

7        20  ^ 

J  1149 

Bary 

5 

March  25 

13     54 

5        29  S 

2  1151 

Eimbeck 

3) 

Aug.    28 

12       4 

4        29  J» 

S  1153 

Augsburgh 

© 

Jan.      26 

0    42 

11         —  > 

S  1154 

Paris 

D 

June     36 

16       1 

Total     s 

290 


Of  Eclipses. 
STRUYK's  CATALOGUE  OF  ECLIPSES. 


S  Aft. 
ijChr. 

Eclipses  of  the  Sun 
and  Moon  seen  at 

M.andD. 

Middle 

H.   M. 

Digits     S 
eclipsed.    > 

S  1154 

^aris 

D 

Jec.     2  1 

8    30 

4        22^ 

Jj  1155 

Auranches 

D 

une     16 

8     45 

0        53  S 

5  1160 

tome 

D 

Aug.    18 

7    53 

6        49  > 

S  1161 

tome 

D 

Vug.      7 

8     11 

Total      c 

S  1162 

irfurd 

D 

Feb.       1 

6    40 

5         56  S 

>  1162 

irfurd 

July      27 

21     30 

4        11  S 

?  1163 
S  H61 

Vlont  Gassini 
Milan 

f 

July        3 
June       6 

7    46 
10      0 

2          0? 
Total     S 

S  1168 

Condon 

Sept    18 

14      0 

Total     S 

J  nr2 

Cologne 

3) 

Jan.      11 

13     31 

Total    J 

?  lire 

\uranches 

D 

April  25 

7      2 

8          6? 

s  lire 

Auranches 

D 

Oct.     19 

11     20 

8        53  S 

S  lira 

Cologne 

D 

March  5 

setting 

7        52  S 

?  iirs 

Auranchea 

D 

Aug.    29 

13    52 

5        31  J 

<  iirs 

Cologne 

© 

Sept.    12 

10        51  s 

S  nr9 

Cologne 

Aug.    18 

14    28 

Total     S 

>  1180 

Auranches 

© 

Jan.     28 

4    14 

10        34  J 

$1181 

Auranches 

(& 

July      13 

3     15 

3        48  ^ 

S  1181 

Aaranches 

j) 

Dec.    22 

8     58 

4        40  S 

S  1185 

themes 

© 

May      1 

1    53 

9          OS 

J  1186 

[Cologne 

April     5 

6    — 

Total     S 

?  11S6 

Frankfort 

© 

April  20 

7    19 

4          OS 

s  H87 

Paris 

D 

March25 

16     17 

8        42  J 

s  ii8r 

J  Ild9 

England 
England 

Sept.      3 
Feb.       2 

21    54 
10    — 

8           6? 
9        —  S 

5  1191 

England 

ATi 
W 

June     23 

0    20 

11        32  > 

S  H92 

France 

D 

Nov.    20 

14     — 

6        -^ 

S1193 

France 

D 

Nov.    10 

5    27 

Total     S 

>  1194 

London 

© 

April   22 

2     15 

6        49  S 

v  1200 

London 

D 

Jan.        2 

17       2 

4         35  > 

S1201 

London 

June     17 

15       4 

Total     s 

S  1204 

England 

D 

April    15 

12    39 

Total     S 

?  1204 

Saltzburg 

D 

Oct.     10 

6    32 

Total     S 

S  1207 

Rhemes 

© 

Feb.     27 

10    50 

10        20  J 

S  1208 

Rhemes 

D 

Feb.       2 

5     10 

Total     ? 

S  1211 

Vienna 

Nov.     21 

13    57 

Total     S 

?  1215 

Cologne 

D 

4archl6 

15     35 

Total     S 

C  1216 

icre 

© 

leb.      18 

21     15 

11        36  J 

S  1216 

Acre 

D 

/larch  5 

9    28 

7         4? 

J  1218 

Damictta 

D 

July        9 

9    46 

11         31  S 

<  1222 

Rome 

D 

•Jet.     22 

14    28 

Total     J 

S  1223 

Colmar 

April   16 

8     13 

11         0  ? 

S  122  H 

Naples 

Dec.    27 

9     55 

9        19  w 

>  U30 

Naples 

May     13 

17     — 

Total     S 

J  1230 

London 

Nov.    21 

13     21 

9        34  J 

?>>2 

Rhemes 

© 

Oct.     15 

4    29 

4        25  I 

Of  Eclipses, 
STRUYK's  CATALOGUE  OF  ECLIPSES. 


291 


s'Aft.  1 
S  Chr, 

Eclipses  of  the  Sun 
and  Moon  seen  at 

M.andD. 

Middle 
H.    M. 

Digits   'S 
eclipsed.  / 

s 

__ 

•s 

S  1245 

Rhemes 

© 

uly      27 

17      47 

6     —  s 

>  1248 

London 

3) 

une       7 

8      49 

Total    S 

S  1255 

London 

D 

luly      20 

9      47 

Total    < 

>  1255 

Constantinople 

(v) 

Dec.     30 

2      52 

Annul.  £ 

S  1258 

Augsburgh 

5 

May      IS 

I       17 

Total   s 

^  1261 

Vienna 

X.V 

March  3  1 

22      40 

9       8S 

<  1262 

Vienna 

D 

March    7 

5      50 

Total    s 

?  1262 

Vienna 

D 

\ug.     30 

14      39 

Total   ^ 

S  1263 

Vienna 

3) 

Feb.      24 

6      52 

6     29  S 

!>  1263 

Augsburgh 

Aug.       5 

3      24 

11      17S 

S  1263 

Vienna 

D 

Aug.     20 

7      35 

9        7s 

I*  1265 

Vienna 

D 

Dec.     23 

16      25 

Total   S 

S  126* 

Constantinople 

May      24 

23      11 

11      40  < 

Ij  1270 

Vienna 

© 

March  22 

18      47 

10     40  > 

S  1272 

Vienna 

D 

Aug.     10 

7      27 

8      53  S 

ij  1274 

Vienna 

D 

Jan.      23 

10      39 

9      25  Jj 

S  1275 

Lauben 

D 

Dec.       4 

6      20 

4      29  S 

^  1276 

Vienna 

]) 

Nov.     22 

15     — 

Total   ^ 

S  1277 

Vienna 

D 

May       18 

.  

Total    S 

<J  1279 

Franckfort 

(v) 

April    12 

6      55 

10       6  «J 

S  1280 

London 

D 

March  17 

12      12 

Total    S 

^  1284 

Reggio 

D 

Dec.     23 

16      H 

9   13  J; 

S  1290 

Wittemburg 

CD 

Sept.       5 

19      37 

10     30  S 

S  1291 

London 

j 

Feb.      14 

10        2 

Total   s 

S  1302 

Constantinople 

D 

Jan.       14 

10     25 

Total   S 

?  1307 

Ferrara 

(v) 

April      2 

22      18 

0     54  S 

S  1309 

London 

D 

Feb.      24 

17      44 

Total    > 

S  1309 

Lucca 

D 

Aug.    21 

10      32 

Total    S 

S  J310 

Wittemburg 

£ 

Jan.       3  1 

2        2 

10     10  ^ 

S  1310 

Torcella 

D 

Feb.      14 

4        8 

10     20  S 

S  1310 

Torcella 

D 

Aug.     10 

15      33 

7      16  Jj 

S  1312  Wittemburg 
S  1312;Plaisance 

D 

July        4 
Dec.      14 

19     49 

7      19 

3     23  S 
Total    Ij 

S  1313  Torcello 

D 

Dec.       3 

8      58 

9      34  S 

S  1316 

Modena 

D 

Oct.         1 

14      55 

Total    JJ 

S  1321 

Wittemburo; 

June     25 

18        1 

11      17  S 

J  1323  Florence 

D 

May     20 

15     24 

Total   > 

S  1324 

Florence 

D 

May        9 

6        3 

Total    S 

S  1324 

Wittemburg 

April    23 

6     35 

8       8  £ 

Jj  1327!Constantinople 

D 

Aug.    31 

18      26 

Total   \ 

S  1328  Constantinople 

Feb.      25 

13      47 

11     —  S 

$  13  30;  Florence 

3) 

June     SO 

15      10 

7     34  Sj 

S  1330  Constantinople 

(D 

July       16 

4        5 

10     43  S 

Ij  1330  Prague 

Dec.      25 

15      49 

Total    § 

S  1331  Prague 

(D 

Nov.     29 

20     26 

7     41  S 

S  1  331  1  Prague 

Dec.      14 

18     — 

11     —  £ 

292 


Of  Eclipses, 

S TRUYK's  CATALOGUE  OF  ECLIPSES. 

%# 


S  Aft. 
S  Chr. 

Eclipses  of  the  Sun 
and  Moon  seen  at 

M.andD. 

Middle 
H.    M. 

Digits    S 
eclipsed.  Jj 

S  1333 

Wittemburg 

© 

viay       1  4 

3     — 

10      18  !j 

S  1334 

Cesena 

D:  April    19 

10     33 

Total    S 

S  1341 

Constantinople 

D  Nov.     23 

12      23 

Total    s 

£  1341 

Constantinople 

©;DCC.     8 

22      15 

6     30  S 

S  1342 

Constantinople 

D  May      20 

14      27 

Total    s 

S  1344 

Alexandria 

©Oct.         6 

18      40 

8      55  J 

S  1349 

Wittemburg 

D  June      30 

12      20 

Total    < 

S  1354 

Wittemburg 

©  -Jept.     16 

20      45 

8     43  S 

5  1356 

Florence 

J>  Feb.       16 

11      43 

Total    <. 

S  1361 

Constantinople 

© 

May        4 

22      15 

8      54  S 

S  1367 

Sienna 

D 

Jan.       16 

8      27 

Total    s 

S  1389 

Eugibio 

Nov.        3 

17        5 

Total    S 

S  1396 

Augsburgh 

©  Jan.       1  1 

0      16 

6     22  ^ 

5  1396 

Augsburgh 

D  June     21 

11      10 

Total    S 

S  1399 

Forli 

©Oct.      29 

0      43 

9     -~\ 

S  1406 

Constantinople 

D  :June        1 

13     — 

10     31  S 

«5  1406 

Constantinople 

©June      15 

18         1 

11      38  < 

Jj  1408 

Forli 

©Oct.      18 

21      47 

9      32  S 

?  1409 

Constantinople 

©.April     15 

3        1 

10     48  s 

J  1410 

Vienna 

3  !  March  20 

13      13 

Total    S 

S  1415 

Wittemburg 

©  June       6 

6      43 

Total    s 

J  1419 

Franckfort 

© 

March  25 

22        5 

1      45  £ 

?  142] 

Forli 

J 

Feb.      17 

8        C2 

Total    \ 

S  1422 

Forli 

J 

Feb.        6 

8      26 

11        7$ 

S  1424 

Wittemburg 

© 

June     26 

3      57 

11      20  S 

S  1431 

Forli 

© 

Feb.      12 

2        4 

1      39  £ 

^  1433 

Wittembiirer 

© 

June      1  7 

5     — 

Total   S 

S  1438!  Wittemburg 
S  1442  Rome 

0 

D 

Sept.     18 
Dec.      17 

20      59 
3      59 

8       7S 
Total    S 

S  1448 

Tubing 

© 

Aug.     28 

22     23 

8     53  \ 

S  1450 

Constantinople 

D 

July      24 

7      19 

Total    S 

S  1457 

Vienna 

D 

Sept.       3 

11      17 

Total    £ 

<J  1460 

Austria 

D 

July        3 

7     31 

5      23  ? 

S  1460 

Austria 

© 

July      17 

17     32 

11      19  £ 

Jj  1460 

Vienna 

D 

Dec.     27 

13      30 

Total   ,S 

S  1461 

Vienna 

D 

June     22J11     50 

Total   J[ 

J  1461 

Rome 

1*L 

Dec.     17 

Total    S 

S  1462 

Viterbo 

D 

June      1  1 

15     — 

7     38  J 

Jj  1462 

Viterbo 

© 

Nov.     2  1 

0      10 

2       6  S 

S  1464 

Padua 

D 

April    21 

12      43 

Total    ^ 

5  1465 

Rome 

© 

Sept.    20 

5      15 

8     46  S 

S  1465 

Rome 

D 

Oct.        4 

5      12 

Total    £ 

^  1469 

Rome 

D 

Jan.      27 

7        9 

Total    S 

S  1485 

,  • 

Nurimburg 

March  16 

3     53 

11     —  § 

\ 


Of  Eclipses. 


1293 


All  the  following  ECLIPSES,  are  taken  from  RICCIOLUS,  except  those 
marked  with  an  Asterisk,  which  are  from  L'Art  de  -verifier  les  Dates. 


>'  Aft. 
S  Chr. 
S  

M.  &  D. 

Middle 
H.    M. 

Digits 
eclipsed 

Aft. 
Chr. 

M.  &  D. 

Middle 
H.   M. 

Digits  "s 

eclipsed  \ 

V  1486 

D 

Feb.      1  8 

5      41 

Total 

1508 

0 

May      29 

6     — 

*           S 

Jj  1486 

© 

March    5 

17     43 

9          0 

1508 

i> 

June      12 

17      40 

Total    J; 

S  1487 

D 

Feb.        7 

15      49 

Total 

1509 

June       2 

11       11 

7       OS 

^  1487 

0 

July       2( 

2        6 

7          0 

1509 

0Nov.     11 

22     — 

s 

S  1488 

D 

Jan.       28 

6     — 

# 

1510 

y 

Oct.      16 

19     — 

*           V 

£  1488 

0 

July         8 

1  7      St. 

4          0 

1511 

D 

Oct.        6 

11       50 

Total    5 

S  1489 

J 

Dec.        7 

17      41 

Total 

1512 

Sept.    25 

3      56 

Total    S 

J;  149G 

0 

May      19 

Noon 

* 

1513 

0 

March    7 

0      30 

6       0  ^ 

S  1490 

j) 

June       2 

10        f 

Total 

1513 

© 

July      30 

1      — 

*           S 

>  149C 

3 

Nov.      26 

18     25 

Total 

1515 

D 

Jan.       29 

15      18 

Total    £ 

S  1491 

0 

March     8 

2      19 

9 

1516 

Jan.       1  9 

6        0 

Total    S 

Jj  1491 

Nov.      15 

18     — 

* 

1516 

D 

July      1  3 

11      37 

Total    < 

S  1492 

0 

April    26 

7     — 

* 

15  1C 

® 

Dec.     23 

3      47 

3       0  S 

>  1492 

© 

Oct.       20 

23     — 

* 

1517 

June      1  8 

16     — 

S 

S  1493 

3) 

April    21 

14        0 

Total 

1517 

D 

Nov.     27 

19     — 

s 

>  1493 

© 

Oct.       1C 

2      40 

8          0 

1518 

May      24 

11      19 

9      11SS 

S  1494 

0 

March     7 

4      12 

4          0 

1518 

0 

June       7 

17      56 

11        OS 

^  1494 

3 

March  2  1 

14      38 

Total 

1519 

® 

May     28 

1     — 

*           S 

S  1494 

D 

Sept.      14 

19      45 

Total 

1519 

5) 

Oct.     23 

4     33 

6       0  S 

!j  1495 

3> 

March  10 

16     — 

* 

1519 

D 

Nov.       6 

6      24 

Total    s 

S  1495 

Aug.     19 

17     — 

# 

152015 

May        2 

7     — 

*           S 

<J  1496 

5' 

Jan.       29 

14     — 

* 

1520 

fe 

Oct.      1  1 

5      22 

3           s 

S  1497, 

]) 

Jan.        18 

6      38 

Total 

1520 

3 

Oct.      25 

19     — 

*           S 

Jj  1497 

0 

July       29 

3        2 

3          0 

1520 

3 

March  2  1 

17     — 

*           / 

S  1499 

5 

June      22 

17     — 

* 

1521 

0 

April      6 

19     — 

*           S 

,5  1499 

0 

Aug.     23 

18     — 

* 

1521 

0 

Sept.     50 

3     — 

*        s 

S  1499 

D 

Nov.      1  7 

10     — 

# 

1522 

D 

Sept.       5 

12      17 

Total    S 

^  1500 

0 

March  27 

In  the 

Night 

1523 

3 

March    1 

8      26 

Total    s 

S  1500 

3 

April     1  1 

At 

Noon 

1523 

3 

Aug.     25 

15      24 

Total    Jj 

<J  1501 

3 

Oct.        5 

14        2 

10       0 

1524 

0 

Feb.       4 

1      — 

S  1502 

3 

May        2 

17     49 

Total 

1524 

3> 

Aug.     16 

16     — 

*           S 

£  1502 

© 

Sept.     30 

19      45 

10       0 

1525 

0  Jan        23 

4     — 

*                 V 

S  1503 

D 

Oct.       15 

12      20 

2          0 

1525 

D 

July         4 

10      10 

Total    > 

^  1503 

D 

March  12 

9     — 

* 

I52o 

5 

Dec.     29 

10      46 

Total    ? 

^  1503 

0 

Sept.     19 

22               —  r 

* 

1526 

D 

Dec.      18 

10      30 

Total    S 

S  1504 

D 

Feb.      29 

13      26 

Total 

1527 

0 

Jan.         2J  3     — 

£ 

S  1504 

© 

March  16 

3     — 

# 

1527 

Dec.       710     — 

\  1505 

5 

Aug.     14 

8      18 

Total 

1528 

0 

May      17 

20     — 

*    S 

lj  1506 

3 

Feb.        7 

15     — 

* 

1529 

D 

Oct.       1  6 

20      23 

11      55  ^ 

S  1507 

© 

July       20 

3      11 

2          0   1530 

© 

March  28 

13     23 

8        4s 

!j  1506 

/*~'S 

Aug.       3 

10     — 

* 

1530 

3 

Oct.        6 

12      1 

Total    ^ 

S  1507 

0 

Jan.       12 

19     — 

* 

153 

3 

April       1 

7     — 

*           S 

^  1508 

0 

Jan.         2 

4     —  — 

* 

1532 

0 

Aug.     30 

0     40 

S 
S 

Of  Eclipses. 
'RICCIGLUS's  CATALOGUE  OF  ECLIPSES. 


S  Aft. 
S  Chr. 

M.  Sc  D. 

Middle 
H.    M. 

Digits 
eclipsed 

Aft. 
Chr. 

M.  Sc  D 

Middle 
H.    M. 

Digits 
eclipsed 

S  1533 

3 

Aug.       4 

11      50 

Total 

1556 

(V) 

Nov.        1 

18        0 

9      41 

S  1533 

© 

Aug.      19 

17     — 

* 

1556 

3 

Nov.      1  6 

12     44 

6      55 

S  1534 

© 

Jan.       14 

1      42 

5      45 

1557 

(Vf 

Oct.      20 

20     — 

* 

S  1534 

3 

Jan.       29 

14     25 

Total 

1558 

3 

April      2 

11        0 

9      50  S 

Ij  1535 

© 

June     30 

Noon 

* 

1558 

© 

April     18 

1      —  — 

*           S 

S  1535 

3 

July       14 

8     — 

* 

1559 

3 

April     16 

4      50 

Total  J 

lj  1535 

© 

Dec.      24|   2     — 

# 

1560 

3 

March  11 

15      40 

4      13  <| 

S  1536 

© 

June      18 

2        2 

8        0 

1560 

Aug.     21 

1        0 

6     22  5 

^   1536 

D 

Nov.     27 

6     24 

10      15 

1560 

3 

Sept.       3 

7     — 

*           S 

S  1537 

3 

May      24 

8        3 

Total 

1561 

© 

Feb.       13 

29     — 

* 

£  1537 

© 

June        7 

8     — 

* 

1562 

©  Feb.        3 

5      — 

S 

S  1537 

3 

Nov.      16 

14      56 

Total 

1562 

3  July       15 

15      50 

Total  J 

^  1538 

3 

May      1  3 

14      24 

2        0 

1563 

(v)!Jan.       22 

19      — 

* 

S  1538 

3 

Nov.        6 

5      31 

3      37 

1563 

© 

June      20 

4      50 

8     38^ 

£  1539 

© 

April      8 

4      33 

9        0 

1563 

3 

July         5 

8        4 

11      34  i 

S  1540 

© 

April      6 

17      15 

Total 

1565 

© 

March    7 

12      53 

^ 

!j  1541 

3 

March  1  1 

16      34 

Total 

1565 

3  May      14 

16     — 

I 

S  1541 

© 

Aug.     21 

0      56 

3 

1565 

^  I  Nov.       7 

12      46 

11      46  J 

^  1542 

3 

March    1 

8      46 

1      38 

1566 

3>|Oct.       28 

5      38 

Total  ^ 

S  154* 

© 

\ug.      10 

17     — 

* 

1567 

©April      8 

23        4 

6     34  s 

Ij  1543 

3 

July       15 

16     — 

* 

1567 

D 

Oct.       17 

13      43 

2      40  S 

S  1544 

3 

Jan.         9 

18      13 

Total 

1568 

© 

March  28 

5      — 

5 

S  1544 

© 

Jan.       23 

21       16 

11      17 

1569 

3 

March    2 

15'    18 

Total  J 

S  1544 

3 

July        4 

8      31 

Total 

1570 

3 

Feb.      20 

5      46 

Total  < 

5  1544 

3 

Dec.     28 

18      27 

Total 

1570 

3 

Aug.     15 

9      17 

Total  J 

!j   1545 

© 

June       8 

20      48 

3      45 

157. 

Jan.       25 

4      — 

*               V 

S  1545 

Dec.      17 

18     —    * 

1572 

Jan.        14 

19      — 

< 

Jj  1546 

<-•• 

May      30 

5      —  (   * 

1572 

| 

fune      25 

9        0 

5      26  V 

S  1546 

Cv 

Nov.     22 

23     —    * 

1573 

June      28 

18     — 

*            < 

!j  1547 

3 

May        4 

0      27]   8        0  1573 

v? 

Nov.      24 

4     —  • 

*           \ 

S  1547 

3 

•)ct.       28 

4      56J11      34 

1573 

© 

Dec.        8 

6      51 

Total  I 

>  1547 

\Tov.      12 

2        9 

9      30 

1574 

3 

Nov.       13 

3      50 

5     21  V 

S  1548 

S 

Ypril       8 

3     — 

* 

1575 

© 

May       19 

8     —  - 

6 

!j  1548 

3 

April    22 

11      24 

Total 

J157o 

T) 

Nov.        2 

5     — 

* 

S  1549 

3 

April     1 

15      19 

2        0 

1576 

3 

Oct.         7 

9      45 

< 

!j  15-49 

^ 

•Oct.         C 

6     — 

* 

1577 

3 

April       2 

8      33 

Total  < 

S   1550 

© 

iVLirch  10 

20     — 

* 

1577 

3 

Sept.     26  !  3        4 

Total  .' 

*ij  1551 

3 

Feb.      20 

8      21 

Total 

1578 

3 

;:cpt.      1513        4 

2      20  < 

S  1551 

;v) 

Au-.     31 

2        0 

1     52 

1579 

© 

i'eb.       15 

5      41 

8      36  < 

vj  1553 

© 

Jan.        12 

22      54 

1     22 

1579 

(S 

Aug.     20 

19        0 

; 

S  1553 

© 

July       10 

«•      

# 

1530 

3 

10        7 

Total  ; 

^  1553 

3 

July       24 

16        0 

0      31 

1581 

3 

Jan.        19 

9      22 

Total  ( 

S  1554 

© 

Jr.  lie      29 

6     -— 

* 

1581 

3 

July       15 

17      51 

Total  | 

S  .l^54 

-i' 

Dec.        t 

13        7 

10      12 

1582 

3 

Jan.         8 

10     29 

0     53, 

S  1  555 

3 

June       4 

15        C 

Total 

1582 

a 

June        9 

17        5 

r     s 

•^   1  5  5  5  j  5o 

Nov.      13 

.19     — 

* 

1583 

3 

Nov.      28  21      51 

Total 

Of  Eclipses. 


RICCIOLUS's  CATALOGUE  OF  ECLIPSES. 


2?& 

JChr. 

M.  Sc   D. 

Middle 
H.    M. 

Digits 

eclipsed. 

Aft. 
Chr. 

|M.  &  D. 

Middle 
II.    M. 

Digits  S 

eclipsed  ^ 

Ij  1584 

© 

May        9 

18      20 

3      36 

1601 

D;  June      15 

6      18 

4      52  £ 

S  1584 

D 

Nov.      17 

14      15 

Total 

1601 

©  June     29 

China 

4      29  S 

5  1585 

© 

April      2 

7     53 

11        7 

1601 

D  Dec.       9 

7       6 

10      53  s 

S  1585 

D 

May      13 

5        9 

6     54 

1601 

a 

Dec.     24 

2     46 

9      52  S 

Ij   1586 

D 

Sept.     27 

8     — 

# 

1602 

© 

May     21  Green] 

241s 

S   1586 

(?••• 

Oct.       12 

Noon 

# 

1602 

3 

June       4 

7      18 

Total  S 

Ij  1587 

5 

Sept      10 

9     28 

10       2 

1602 

© 

June      1  9 

N.Gra. 

5      43  s 

S  1588 

© 

Feb.      26 

1      23 

1        3 

1602 

© 

Nov.      1  3 

Magel. 

3     —  S 

ij  1588 

3 

March  12 

14      14 

Total 

1602 

3) 

Nov.      28 

10        2 

Total   s 

S  1588 

3> 

Sept.       4 

17     30 

Total 

1603 

© 

May      10 

China 

11      2lS 

^  1589 

© 

Aug.      10 

18     — 

# 

1603 

3> 

May      24 

11     41 

7     59  S 

S  1589 

3) 

Aug.     25 

8         1 

3      45 

1603 

© 

Nov.        3 

Rom.  I. 

11      17  J> 

>  1590 

© 

Feb.        4 

5     — 

# 

1903 

D 

Nov.      18 

7     31 

3      26  S 

S  1590 

3 

July       16 

17        4 

3      54 

1604 

© 

April    20 

Arabia 

9      32  J» 

>   1590 

© 

July       30 

19      57 

10      27 

1604 

© 

Oct.      22 

Peru 

6     49  S 

S  1591 

3) 

Jan.         S 

6     21 

9      40 

1605 

D 

April      3 

9      19 

11      49  £ 

!j  1591 

3) 

July         6 

5        8 

Total 

1605 

© 

April    1  8 

Madag. 

5      31  S 

S  1591 

/  •  r*-. 

July       20 

4        2 

I        0 

1605 

3> 

Sept.     27 

4      27 

9      26  ^ 

^  1591 

3 

Dec.      29 

16      11 

Total 

1605 

© 

Oct.      12 

2      32 

9      24  S 

S  1592 

3) 

June     24 

10      13 

8      58 

1606 

© 

March    8 

Mexico 

6        0  £ 

!j  1592 

j) 

Dec.      18 

7     24 

5      54 

1606 

5 

March  24 

11       17 

Total  S 

S  1593 

© 

May      30 

2      30 

2      38 

1606 

© 

Sept.       2 

Magel. 

6     40  J; 

^  1594 

© 

May      1  9 

14      58 

10      23 

1606 

© 

Sept.       2 

Magel. 

6     40  S 

S  1594 

D 

Oct.      28 

19      15 

9      40 

1606 

3 

Sept.     16 

15        6 

Total.  $ 

%  1595 

© 

April      9 

Ter.de 

Fucgo 

1607 

0 

Feb.      25 

21      48 

1      13  S 

S  1595 

J) 

April    24 

4      12 

Total 

1607 

3> 

March  13 

6      36 

1      22  Jj 

S   1595 

© 

May        7 

o     

# 

1607 

© 

Sept.       5 

15      40 

4        7  <» 

£  1595 

© 

Oct.         3 

2        4 

5      18 

1608 

© 

Feb.      15 

at  the 

Antipo.  Jj 

S  1595 

]) 

Oct.       18 

20     47 

Total 

1608 

3 

July      27 

0      30 

1      53  S 

S  1596 

© 

March  28 

In 

Chili 

1608 

© 

Aug.       9 

4      39 

0      40  ^ 

S  1596 

D 

April     12 

8      52 

6       4 

1609 

j) 

Jan.       19 

15      21 

10      32  S 

>  1596 

© 

•)ept.     21 

In 

China 

1609 

© 

Feb.       4 

Fuego 

5   22  i; 

S  1596 

3) 

•)ct.         6 

21       15 

3     33 

1609 

D 

July      16 

12        8 

Total   S 

>  1597 

vlarch  16 

St.  Pet. 

Isle 

1609 

® 

July      30 

Canada 

4      10  % 

S  1597 

© 

*>ept.     1  1 

Picora 

9      49 

1609 

© 

Dec.     26 

19     — 

5      50  ^ 

Jj  1598 

3) 

Feb.      20 

18      12HO      55 

1610 

3) 

Jan.         9 

1      31 

Total    5 

S  1598 

© 

March    6 

22      12 

11      57 

1610 

© 

June     20 

Java 

10     46  S 

%  1598 

j) 

Aug.      1  6 

1       15 

Total 

1610 

D 

July        5 

16      58 

11      1S2 

S   1596 

© 

Aug.     3  1 

Magel. 

S      34 

1610 

© 

Dec.     15 

Cyprus 

4      50  J 

Ij  1599 

9 

Feb.       10 

18      21 

Total 

1610 

3) 

Dec.     29 

16      47 

4      23  s 

S  1599 

© 

July      22 

4     31 

8      18 

1611 

© 

June      10 

Calilbr. 

11      30  S 

I}  1599 

3) 

Aug.       6 

Total 

1612 

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May      14(10     38 

7      22  v 

S  1600 

© 

Jan.       15 

Java 

11      48 

1612 

© 

•lay      29 

23      38 

r    H  s 

Ij  1600 

3) 

Jan.       30 

6      40 

2      5* 

16  i  2 

D 

.'ov.        8 

3     22 

9      49  > 

S  1600 
%  1601 

© 
0 

July       10 
Jan.         4 

2      10 
Ethiop. 

5      39 
9      40; 

1612 
1613 

© 

© 

Nov.      22 
April    20 

Magel. 
Magel. 

*.m     O's 

lanica.    £ 

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**                                                                                                                                                                                                                                                  ^   *J 

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296  Of  Eclipses. 

RICClOLUS's  CATALOGUE  OF  ECLIPSES. 


S*Aft. 

S  Chr. 

"./•- 

r*rj~*r^^- 

M.and  D. 

./-v./'V^/^/^ 

Middle 
M.      M. 

»\y-,r\yx/-,x'-*--r«x 

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^r-s 

-^^rv-A^-. 

M.and  D. 

Mldle      Dig-its     S 
I.    M.'  eclipsed.  V 

S  1613 

•jj 

May      4 

0        35 

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1625 

© 

./iarch  b 

Florida                   £ 

S  1613 

<) 

May     19 

East 

Partary 

1625 

J) 

viarcn23 

14      11    2         11  S 

?  1613 

4.'0 

Oct.      13 

South 

Arm  r. 

1625 

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St.  Pe'ter's  Isle  S 

^1613 

f 

Oct.     28 

4        19 

Total 

1625 

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,ept.     16 

11      41    5           6  c 

S  1614 

w 

April     fc 

N.  Gui. 

8        44 

1626 

3 

i-'eb.     25 

Madag    8        27  S 

5  1614 

~j) 

April    23 

17         36 

5        25 

1626 

^ 

Aug.       7 

7      48 

0         25  S 

J  1614 

Oct.       3 

0         57 

5           2 

1626 

© 

Aug.     21 

In 

Mexico   J 

S  1614 
S  1615 
J  1615 

T)  <  )ct.      17 

(f)  March  29 
^  Sept.    22 

4        58 
Goa 

Salom 

4         56 

10        38 
Isle 

1627 
1627 
1627 

5 

Jan.      30 
I-eb.     15 
July      27 

11      38 
Magel 
9       4 

10     21  <; 

Itnica        <» 
Total     S 

SifilS* 

M  .rch  3 

I         58 

Total 

16,7 

S) 

/\ug.    11 

Tenduc 

10          0  J 

S  1616 

March  17 

Mexico 

6        47 

1628 

© 

.ian.        6 

'1  'endue 

5         40  t 

S  1616 

Aug.     26 

15         35 

Total 

1628 

Jan,     20 

10      11 

Total     S 

J  16]6 

Sepr.    10 

Ma  gel. 

10        33 

[62i 

.'?•: 

July       1 

C.Good 

Hope       S 

S  1617 

•  ''•7) 

Feb.        5 

Mage! 

anica 

1  Si 

5" 

July      16 

11      26 

Total     J 

S  1617 
>  1617 

j> 

<•-.-•> 

Feb.     20 
March  6 

1         49 

22        — 

Total 

1621 

162v 

© 

Oec.     25jlnEug 
Ian.        91      36 

and          ? 
4        27  "S 

c  1617 

i 

Aug.       1 

Biarmia 

# 

1629 

.Tf 

June     11 

Gange 

J.1        25  S 

S  1617 

Aue.    16 

8         22 

Total 

1629  © 

Dec.     H 

Peru 

10         14  J 

S  1618 

f'janT     26 

Maarei 

.anica 

1630J  T) 

May     25 

17      56 

6          0  s 

J  1618 

(Feb.      9 

3        29 

2         57 

1630 

© 

lune     10 

7      47 

9           8  S 

^  1618 

D 

July      21 

Mexico 

16,j(j 

2 

\rov.     19 

11      24 

9         27  S 

S  1619 

S 

Jan.      15  !    Caliior 

aia 

1630 

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Dec.      3 

N.  Gui. 

10         10  t 

S  1619 

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June     2G 

12        40 

5         10 

1631 

© 

-vpril   30 

Antar. 

Circle       s 

J  1619 

© 

Jaly      11 

Africa 

11         39 

163 

Way      15 

8      15 

Total    S 

<  1619 

5 

Dec.    20 

15        53 

10         47 

163  1 

© 

Oct.      24 

C.Good 

Hope      J 

S  1620 

© 

May    31 

Arctic 

Circle 

1631 

"D 

Mov.       8 

12       0 

1-  Total     ^ 

S  1620 

5 

June     14 

13        47 

Total 

1632 

© 

Apr.      19 

C.Good 

Hope      S 

J  1620 

© 

June     29 

Mattel. 

7        20 

1632 

D 

May       4 

1      24 

6        35  S 

S  1620 

}  (Dec.      9 

6        39 

Total 

1532 

© 

Oct.      13 

Mexico 

8         37  J 

S  16^0 

fv) 

Dec.    23 

Mag?l 

lanica 

1532 

<  )ct.     17 

12      2.3 

5        31  c 

J  1621 

3) 

May     20 

14         54 

10         44 

1633 

npril     8 

5      14 

4        30  S 

<  1621 

5 

June       3 

19         42 

9         53 

1633 

Oct.       3 

Maldiv. 

Total     S 

S  1621 
S  1621 

3 

Nov.    13 
Nov.    2.s 

Mage) 
15        43 

lanica 
3        2H 

1634 
i  'i34 

1 

March  14 
March  28 

9      35 
Japan 

11         18  y 
10         19  w 

May     10 

C.  Yen! 

U         J* 

Io.i4 

3)  ISept.      7 

5        0 

Total    S 

lj  1622 

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Malar 

c  i  In. 

1634 

Sept.    22 

C.G.FL 

9        54  J> 

S  1623 

5 

\pril    1  4 

7         19 

10         5'i 

1635 

Feb.      17 

Antar. 

Circle       <J 

S  1523 

© 

April  29 

1635|5 

March    3 

9      26 

Toial     S 

J  1623 

Oct.       ft 

0        22 

8        35 

1  o.>5  (v) 

March  U 

.vlexico 

0        16  S 

^  1623 

(V) 

Oct.     23 

Califor. 

10        46'|1635|(3 

Aug.     12 

Iceland 

5           07 

S  1624 

©May    18 

N.  Zem. 

6          0  163.5!  J 

Aug.    27 

16       4 

Total     < 

£  1S24 
J  1624 

1 

\pril     3 
April    17 

7          9 
Ant'.r. 

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Feb.        £ 
Feb.     20 

In 

11      34 

Peru     S 
3        23  S 

S 

S  1624 

© 

Sept.    12 

Mag.-! 

i  mica     \  1636  (v) 

\ug-. 

Tartan 

U        20^ 

S  1624 

5 

Sept.    2C 

8         5J 

Total    .1636  j> 

Aug.    1- 

34 

1        25  J 

CJf  Eclipses. 
KICCIOLUS's  CATALOGUE  OF  ECLIPSES. 


J  Aft. 
S  Chr. 

M.  &  D. 

Middle 
H.    M. 

Digits  j|Aft. 
eclipsed  Chr. 

© 
© 

5 

© 

© 
D 
© 
© 
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© 
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© 
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J  1637 
<J  1637 
J*  1638 
S  1638 
jj  1638 
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S  1639 
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>  1640 
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S  1641 

Jj  i64i 

S  1641 
>  1642 
S  1642 
£  1642 
S  1642 
Jj  1643 
S  1643 
Jj  1643 
S  1643 
Ij   1644 
S  1644 
Ij  1645 
S  1645 
Ij  1645 
S  1645 
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S   1646 
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J   16-1-6 
3  1647 
S  1647 
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S   1648 
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© 
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•uiy       21 
Dec.     31 
1  ji.        14 
,une      25 
July       11 
Dec.        5 
Dec.      20 
Jan.         4 
J  une        1 
June      15 
Srov.     24 
Dec.       9 
May      20 
Nov.      1  3 
April    25 
May        9 
Oct.       18 
Nov.        2 
March  30 
April    1  4 
Sept.     2.) 
Oct.         7 
March  19 
April      3 
Sept.     1  2 
Sept.     27 
March    8 
Aug.     3  1 
Feb.      10 
Feb.      26 
Aug.       7 
Aug.     21 
Jan.        1  6 
fcarj.       30 
Uily       12 
July       27 

s 

20 

'  ':  \  i  V                   2 

Dec.     25 

•         5 
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NOV.      29 
Dec.      13 

May      25 

Cain 
Jucutan 

0      44 
Persia 

20      17 
C  Mag 
£  ellan 
15      16 
Tartary 
5      29 
2      41 
Magel. 
11      57 
NT.Spa. 
Peru  2 
I 
Peru 
8      19 
18      46 
Estod. 
14      31 
Magei 
16      45 
13      53 
.31       10 
17        0 
7      38 
6      20 
IS      10 
7      45 
Rom.  I. 
2         4 
0      35 
Str.of 
18      1  i 
6      57 
6        £ 
12       10 
9      43 
0        9 
13      3f> 
0      55 
1  3      2.3 
19      17 
21      48 
15      20 

boya 

10     45 
9      45 
Total 

9         5 
2      10 
Total 
0      30 
10      40 
11        9 
11        0 
3      46 
10      30 
10      3o 
9      4, 
10       16 
6      31 

j  1649 
J1649 
|1649 
1650 
1650 
1650 
1  650 
1651 
1651 
1652 
1652 
1652 
1652 
1653 
1653 
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1654 
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1655 
1655 

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1655 

1657 
1657 
1658 
165ft 
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1658 
1  6  5  9 
1659 
1  659 
1659 
1060 
1660 
1660 
1  660 
1661 
1661 

June        9 
Nov.        4 
Nov.      1  8 
April    30 
May      1  5 
Oct.       24 
Nov.        7 
April     1' 
Oct.       l-l 
:h  24 
April      7 
Sept.     ir 

'  }  P  *~                  c"* 

i-'eb.      27 
March  13 
Aug.     22 
Sept.       6 
Feb.       16 
MiiTcii    2 
Aug.     1  1 
Aug.     27 
Feb.        6 
\«g.       1 

Jan.       1  1 
July         6 
juiy       21 
Dec.     30 
•      11 
j'une     25 
Dec.       4 
Dec,     2( 
May      3  1 
June      M 
Nov.       9 
Nov.     24 

n 

M;ty        20 
Oct.       29 
Nov.     1  l- 
April    21 
Oct.         3 
Oct.       18 
Nov.       2 
vlarch  29 
April     R 

ArctC. 

2       10 
19      56 
5      5  4 
8      37 
17      17 
20      29 
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1  6      52 
22      40 
7      27 
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4        0  £ 
3      16  S 
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9      59  t[ 

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23     45 
9       10 
19      25 
22      24 
1  1      40 
2      37 
14      19 
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3      17 
11      43 
23      30 
11      20 
9      35 
20        O 

r    47 

16        0 
22      58 
3      56 
11      36 
8      34 
17        4 
16      16 
4      25 
11      58 
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0      32 
3      4c 
22      32 
4     28 

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3      14  s 
2     28  £ 
1      53  Ij 
4      20  Jj 

*           S 
10        0  s 
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4        0 
Total 
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3        <; 

6        0 

Total    S 

8      52 
10      46 
Total 
4      40 
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Total 

Total  -*J 

S 

0      10  S 

s 

Total 

8        5> 

s 

4      47 

5      5  2  % 

9      51  ^ 
Total    s 

4      28 

Total    S 

7      40 
Total 

S 

s 

29S 


Of  Eclipses. 


RICCIOLUS's  CATALOGUE  OF  ECLIPSES. 


5  Aft. 
S  Ciu. 

M.andD. 

Middle 
H.     M. 

i      ;is 
eclipsed. 

Aft. 
Chr. 

M.andD 

Middle 
H.    M. 

Digits  S 
eclipsed  <* 

S  1661 
5  1661 
S  1662 
^  166. 
V  iiv-3 
S  i663 
S  1663 
Jj  1663 
S  1664 
!»  1664 
S  1664 
!j  1664 
S  166.3 
Jj  166., 
S  1665 
!j  1660 
S  166& 
\  1667 
S  1667 
!j  1667 
S  1668 
!j  1668 
S  1668 
!>  1668 
S  1669 
^  1669 
S  1670 
I]  1670 
S  1670 
!j  1670 
S  1671 

S  1671 
lj  1672 

S  1672 

S 

S  1672 
S  1673 

!  i 

S    167:; 

J  1675 
V  1676 

© 
3) 

© 

& 

3> 

© 

© 

© 

.-•  •, 

3 
© 
3 
© 
© 

© 

© 
© 

© 
3 

© 
© 
© 

f 
© 
© 
© 

3 

® 

© 
3 

© 

3 
© 

j 

*  .'-••' 

Sept.     23 
Oct.        7 
March  19 

Feb.      2  1 
a     . 
Aug.     18 
Sept.       1 
Jan.       27 
Feb.      1  1 
h:;y       22 
Aug.     20 
Jan.       3i 
July       12 
July      26 
Jan.         4 
July         1 
June        5 
July      21 
NTov.     25 
Mav       10 
May      25 
Kov.        4 
Nov.      1  8 
April    29 
Oct.      24 
April     1  9 
Sept.     10 
Sept.     28 
Oct.       13 
April      8 
Sept.       2 
Sept.     1  8 
Feb.      28 
March  13 

•up\.       C 
Feb.        6 
Aug.     1  1 

Jan.       21 
'  .  b. 
July       17 
Jan.        11 
'"'ii        2^ 
July        6 
June      1C 

1      36 
14      51 
15        8 
1        8 
16      11 
5      47 
8      45 
8        8 
20      40 
3      16 
14     48 
22      10 
18      47 
7      48 
13      31 
31      33 
19        0 
Noon 
2      32 
11      30 
Setting 
16     26 
2      53 
3      54 
13      18 
10      13 
7        0 
19        0 
15      45 
12        5 
23      29 
21      25 
7      44 
3      38 
3      17 
6     43 
18      5--. 
7     29 
21      44 
18      22 
9        4 
9      40 
8      29 
;o     36 
16     31 
21      26 

1  1       1  9 

7         4 

3      14 

676 

1671 

1677 
167W 
1678 
1679 
1  679 
1680 
1680 
1680 
1681 
1681 
1681 
1682 
1682 
1683 
1683 
1683 
1684 
1684 
1684 
1684 
,1685 
1685 
1685 
J1686 
il686 
',1686 
11687 
1687 
i!687 
,1688 

'1688 

1689 
169G 
1690 
1690 
1690 
1691 
169; 
1692 
1692 
1692 

3 
© 
© 
3 
3 
3 
© 
3 
© 
© 
3 
© 
3 
© 
3 

© 
3 

© 

3 
© 
3 
© 

3 
© 
3 
3 
© 
3 
© 
3 

© 
3 
© 

© 

© 
3 

© 

June  25 
Dec.  4 
Nov.  24 
May  16 
May  6 
Oct.  29 
April  10 
May  25 
March  29 
Sept.  22 
March  4 
March  19 
Aug.  28 
Sept.  11 
Feb.  2  1 
Aug.  16 
Jan".  27 
Feb.  9 
Aug.  6 
Jan.  1  6 
June  26 
July  12 
Dec.  21 
Jan.  '  4 
June  16 
Dec.  10 
May  2  1 
June  6 
Nov.  29 
May  1  1 
May  26 
April  15 
April  2: 
Oct.  9 
Oct.  25 
April  4 
Sept.  28 
March  10 
March  24 
Sept.  3 
Sept.  1  8 
Feb.  27 
Aug.  23 
Feb.  2 
Feb.  If 
July  27 

6     26 
20     52 
12        5 
16      25 
5      30 
9      17 
21        0 
11      53 
23      22 
7      57 
Noon 
13     43 
15      22 
15      43 
12      28 
18      56 
I      35 
3      39 
20      36 
6      34 
15      18 
4      26 
11      18 
16        0 
6        0 
11      26 
17        9 
Noon 
12      22 

14     — 
7        4 
16     27 
Noon 
19     4C 
7      42 
15      46 

L 

S 

8      15  S 

Total  £ 

1  i;tai 

S 

~  S 

4      34 

10      35  !j 

Total  £ 
Total   S 
10     30  5 

s 

0      10 

11       10 

s 

~  s 

9      32 
9      50 
6      45 

9        7 

1      35  > 
Total  s 
9      45  S 

Total   S 
Total   $ 
6     49  5 

S 

'Total    < 
Total   ^ 

Total 

11       14 

2      42 
17      30 
5      51 
3      20 
17     31 
16        9 

5     43  S 

11      21 

'i  otai 
Total 

TotaJ 

4      3-1 

S 

E^! 

Total  ^ 

Of  Eclipses, 


299 


RICCIOLUS's  CATALOGUE  OF  ECLIPSES. 


s'Aft. 
\  Chr. 

M.andD. 

Middle 
H.    M. 

Digits, 

eclipsedj 

Aft. 
Chr. 

M.andD. 

Middle 
II.    M. 

Di-its  S 
eclipsed  JJ 

>  1693 

t    1  fiQ^ 

5 

Tk 

Jan.      21 

17     2j 

1  oUii 

1696 
1  fiQ7 

© 

/rr. 

Nov.     23 

A  i-ji'i  1      2() 

17     32 

U<IO 

S 

>  1694 
S  1694 

S    1  fiQ/l 

J> 

D 

© 

TV 

Jan.       1  1 
June     22 

liilv           6 

Noon 

4     22 
13      51 

6     22 

a     47 

1697 
1697 
1698 

W 

3 

3 

^ 

May        5 
Oct.      29 
•\nril     10 

18      27 
8      44 
9      13 

88      45  £ 

C     1  AQ  5 

J 

,V,N 

Vlav           1  1 

fi        ^ 

1  fiQR 

^ 

/TT-, 

Ort           ^ 

15      99 

I 

£  1695 

^> 

7i 

May      28 

Noon 

1699 

(i) 

^ 

March  15 

8      14 

9        7^ 

S  1695 

i       1  fiO  S 

Ji 

D 
r^ 

Nov.     20 
DPP         5 

8        0 
17         7 

6      55 

1699 
1  fiQQ 

JJ 

© 

March  30 

Cif*nt          c 

22        0 

23      22 

_| 

S  1696 

7    i  cq  r 

w 

j) 

'.t\ 

May      16 

IVTnv         ^0 

12      45 
1  9       «ifi 

Total 

1699 
1  7nn 

3 
© 

Sept.    23 

22      38 
9O       1  1 

9      58  S 

S  1696 

© 

5 

Nov.        8 

17      30 

Total 

1700 

3 
3 

Aug.     29 

1      42 

S 

'  S 

The  Eclipses  from  STRUYK  were  observed  ;  those  from  RICCIOLUS 
calculated  :  the  following  from  L?Art  de  -verifier  les  Dates  are  only  those 
which  are  visible  in  Eurojie  for  the  present  century :  those  which  arc 
tota,!  are  marked  with  a  T. ;  and  M.  signifies  Morning,  A.  Afternoon. 


VISIBLE  ECLIPSES  FROM 


*.<• 


1700  TO    1800. 

# 


5  Aff 

Months 

Time    ot 

Aft 

|  Months 

Time  of  S 

^    jfVlL* 

^Chr. 

s 

and 
Days. 

the     Day 

or  Night. 

£\l\>* 

Chr. 

and 
Days. 

the  Day    s 
or  Night.   S 

S  1701 

J 

Feb.      22 

11     A. 

1715 

© 

May        3 

9     M.T.  S 

S  1703 

3 

Jan.         3 

7     M. 

1715 

D 

Nov.      1  1 

5     M.     s 

S  1703 

2 

June     29 

i   M.y. 

1717 

March  27 

3     M. 

lj  iros 

3 

Dec.     23 

7    M.T. 

1717 

3 

May      20 

6     A.       ^ 

S  1704 

3 

Dec.      11 

7     M. 

1718 

Sept.       9 

8     A.  T.  \ 

vj  1706 

j) 

April    28 

2     M. 

1719 

•j) 

Aug.     29 

9     A.      5 

S  1706 

© 

May      12 

10     M. 

1721 

j 

Jan.       13)   3     A.       £ 

^  1706 

3 

Oct.      2  1 

7     A. 

1722 

3 

June     29 

3     M.      S 

S  1707 

April    17 

2     M.2". 

1722 

© 

Dec.       8 

3     A.       S 

S  1708 

3 

April      5 

6      M. 

1722 

3 

Dec.     22 

4     A.       S 

^  1708 

© 

Dec.      14 

8      M. 

1724 

© 

May     ~2 

7     A.T.  J> 

^  1708 

3 

Sept.     29 

9      A. 

1724 

Nov.       1 

4     M.      S 

S  1709 

^~- 

March  1  1 

2     A. 

1725 

3 

Oct.      21 

7    A.    J; 

Ij  1710 

Feb.      1  3 

11     A. 

1726 

© 

Sept.     25 

6     A.      S 

S  1710 

© 

Feb.      28 

1     A. 

1726 

3 

Oct.       1  1 

5   M.    !; 

S  1711 

© 

July       15 

8     A. 

1727 

© 

Sept.      15 

7     M.      S 

S  1711 

3 

July       29!   6     A.T. 

1729|3 

Feb.      1  3 

.6     A.T.  S 

S  1712 

3> 

Jan.      23    8     A. 

|1729 

3 

Aug.       9 

1     M.     < 

S  1713 

3 

June       8    6     A. 

|l730 

3 

Feb.        4 

4     M.     S 

<,  1713 

3 

Dec.       2,  4     M. 

!173l 

3 

June     20 

2     M.     i 

,«                        s                                                                                    -f/ 

9f  Eclipses* 

VISIBLE  ECLIPSES  FROM  1700  TO 


5  Ait. 

Months 
and 

Time    of 
the     Day 

Aft. 

01  Kr 

Months 
and 

Time    ol  S 
ne     Day  v, 

\ 

Days. 

or  Night. 

onr. 

Days. 

or  Night.  S 

« 

S  1732 

D 

Dec.       1 

10     A.T. 

1794 

0 

\pril      l 

o    M.     J 

^  1733 

0 

May      13 

7     A. 

1764 

J> 

\pril    16 

1     M.     s 

S  1733 

D 

May      28 

r    A. 

1765 

0 

March  2  1 

2     A.      J» 

£  1735 

D 

Oct.         2 

I     M. 

1765 

(••j 

Aug.     16 

5      A.       s 

S  1736 

3 

March  2  6 

12    A.r. 

1766 

j 

•eh.      24 

7     A.      S 

^  1736 

D 

Sept.     20 

3     M.T. 

1766 

(''" 

Aug.       5 

7     A.       s 

S  1736 

© 

Oct.        4 

6     A. 

1768 

J 

an.         4 

5     M.     S 

i  1737 

0 

March    1 

4      A. 

1768 

J) 

'une      30 

4    M.T.  s 

S  1737 

A 

D 

Sept.       9 

4     M. 

1768 

J 

Dec.     23 

4     A.T.  S 

?  1738 

0 

\ug.     15 

1  1      M. 

1769 

<V 

kme        4 

8     M.      S 

S  173, 

5 

Jan.       24 

11     A. 

1769 

3 

Dec.     13 

7     M.      J 

\  173? 

0 

Aug.       4 

5      A 

1770 

0 

yiov.      17 

10     M.     s 

S  1731' 

0 

)ec.     30 

9      M. 

1771 

5 

April    28 

2      M.      X 

lj  174( 

3) 

Jan.       13 

11     A.T. 

1771 

5 

Oct.      23 

5    A.     J; 

S  174! 

j> 

Jan.         1 

12     A. 

1772 

]> 

Oct.  '     1  1 

6     A.T.  S 

<|  174^ 

D 

Nov.        2 

3     M.T. 

1772 

Oct.      2f 

I/)     M.     $ 

<,  174-; 

D 

Aug.     26 

9     A. 

1773 

S3 

March  23 

5     M.     S 

Ij  1746 

D 

Aug.     30 

12      A. 

1773 

j) 

Sept.     50 

7     A.      Jj 

S  1747 

3) 

Feb.      14 

5     M.T. 

1774 

March  11 

10    M.     c 

Jj  1748' 

July      25 

11     M. 

1776 

j) 

July      31 

1     M.T.  S 

S  1748 

3 

Aug.       8 

12      A. 

177C 

\L 

Aug.     14 

5     M.     5 

S.  1749 

D 

Dec.     23 

8      A. 

1777 

0 

Jan.         9 

5     A.      S 

^  1750 

{"?} 

Jan.         8 

9     M. 

1778 

/v)Uune     2< 

4     A.      ^ 

S  1750 

j) 

June      19 

9    A.r. 

1778 

J> 

Dec.       4 

6     M.      S 

I!  1750 

D 

Dec.      IS 

7     M. 

1779 

3 

May     30 

5      M.T,  % 

S  1751 

j> 

June       9 

2     M. 

1779 

0 

June     14 

8     M.      S 

<J  175i 

3) 

Dec.       2 

10     A. 

1779 

J) 

Nov.     23 

s    A.    J; 

S  175*2 

May      13 

8     A. 

1780 

0 

Oct.       27 

6     A.       S 

v  1753 

5 

Apr.      17 

7     A. 

1780 

J) 

Nov.      12 

4     M.     5 

S  1753 

0 

Oct.      26 

10     M. 

1781 

0 

April    25 

6     A.      S 

S  1755 

j) 

March  28 

1     M. 

1782 

0 

Oct.       17 

8   M.    J; 

S  1757 

D 

Feb.        4 

5     M. 

1782 

5 

April    1~ 

7     A.      S 

<  1757 

j) 

July      30 

12     A. 

1783 

D 

March  Ib 

9    A.r.  J; 

J  1758 

5 

Jan.      24 

7   M.T. 

1783 

2) 

Sept.     l.( 

11      A.7\S 

S  1758 

0 

Dec.     30 

7     M. 

1784 

3 

March    7 

3     M.      < 

S  1759 

0 

June     24 

r    A. 

1785 

0 

:-'cb.        9 

1     A.      S 

$  1759 

0 

Dec.      19 

2     A. 

1787 

j)  |Jan.         3 

12     A.T.  ^ 

S  176C 

May      29 

9     A. 

1787 

(v)Jan.       19 

10     M.      S 

<J  176C 

0 

June      1  3 

7     M. 

1787 

0 

June      15 

5     A.       < 

S  176C 

D 

Nov.     22 

9     A. 

1787 

5 

Dec.     24 

3     A.       S 

^1761 

5 

May      18 

11      A.T. 

1788 

(v". 

June        4 

9      M.      s 

SI  W  i*r 
1  7  0^ 

D 

May        8 

4     M. 

1789 

j 

i\ov.       2112      A.       S 

§  176L 

0 

Oct.       1  7 

8      M. 

1790 

5 

April    28J12     A.T.  $ 

S  176: 

3) 

Nov.        1 

8      A. 

m>c 

D 

Oct.      2: 

i    M.r.  s 

S  176: 

0 

April    1  3 

8     M. 

1791 

0 

April      t 

1     A.      < 

VISIBLE  ECLIPSES  FROM  1700  TO 


$  Aft. 
£  Chr. 

s 

D 
© 
D 

J 

Months 
and 
Days. 

Time  of 
the  Day 

or  Night. 

Aft. 
Chr. 

D 

a 

D 

D 

Months 
and 
Days. 

Time  of    S 
the  Day     < 

or  Night.    S 

S  1791 
Ij  1792 
S  1793 
S  1793 
S  1794 
S  1794 
S  1794 

Oct.      12 
Sept.     16 
Feb.      25 
Sept.      5 
Jan.      31 
Feb.      14 
Aug.     25 

3     M. 
11     M. 
10     A. 
3     A. 
4     A. 

11    ^.T. 

5     A. 

1795 
1795 
1795 
1797 
1797 
1798 
J800 

Feb.        4 
July      16 
July      31 
June     25 
Dec.       4 
May      27 
Oct.        2 

1     M.      S 
9     M.     ^ 

8     A.      S 
S     A.       Z 
6    M.      S 

7    A.r.  £ 

11     A.      S 

328.    A  List  of  Eclipses,  and  historical  Events, 
which  happened  about  the  same  Times,  from  Rio 


But  according  to  an  old  calen* 
Jar,  this  eclipse  of  the  Sun  was  on 
the  21st  of  April,  on  which  day 
the  foundations  of  Rome  were  laid; 
if  we  may  believe  Taruntius  Fir- 


Before  CHRIST. 


'54 


721 
585 


March  19 

May     28 


4.63 


July 


6 

Nov.     19 

April    30 


A  total  eclipse  of  the  Moon.  The 
Assyrian  Empire  at  an  end;  thej&z- 
bylonian  established. 

An  eclipse  of  the  Sun  foretold  by 
THALES,  by  which  a  peace  was 
brought  about  between  the  Medes 
and  Lydians. 

An  eclipse  of  the  Moon,  which 
was  followed  by  the  death  of  CAM- 

UYSES. 

An  eclipse  of  the  Moon,  which 
was  followed  by  the  slaughter  of 
the  Sabines,  and  death  of  Valerius 
Public  'o/a. 

An  eclipse  of  the  Sun.  The 
Persia?!  war,  and  the  falling.  off  of 
the  Persians  from  the  Egyptians. 


eclipse. 


302 


Of  Eclipses. 


Before  CHRIST. 
April    25 


An  eclipse  of  the  Moon,  which 
was  followed  by  a  great  famine  at 
Rome ;  and  the  beginning  of  the 
Peloponnesian  war. 

431  August  3  A  total  eclipse  of  the  Sun.  A 
comet  and  plague  at  Athens*. 

413  August^l  A  total  eclipse  of  the  Moon.  Ni- 
dus with  his  ship  destroyed  at  Sy- 
racuse. 

394  August  14  An  eclipse  of  the  Sun.  The 
Persians  beat  by  Conon  in  a  sea-en- 
gagement. 

168  June  21  A  total  eclipse  of  the  Moon.  The 
next  day  Perseus  King  of  Macedo- 
nia was  conquered  by  Paulus  Emi- 
.  lius. 

After  CHRIST. 

59  April  30  j  An  eclipse  of  the  Sun.  This  is 
reckoned  among  the  prodigies,  on 
iccount  of  the  murder  of  Agrippi- 
nus  by  Nero. 

237  April    12        A  "total  eclipse  of  the  Sun.     A 
sign  that  the  reign  of  the  Gordiani 
vould  not  continue  long.    A  sixth 
persecution  of  the  Christians. 
306  July     27        An  eclipse  of  the  Sun.  The  stars 
were  seen,  and  the  Emperor  Con- 
stantius  died. 

840  May  4  A  dreadful  eclipse  of  the  Sun. 
And  Lewis  the  Pious  died  within 
six  months  after  it. 

1009 An    eclipse  of  the   Sun.      And 

Jerusalem  taken  by  the  Saracens. 
1133  August  2       A  terrible  eclipse  of  the  Sun.  The 
stars  were  seen.     A  schism  in  the 
church,  occasioned  by  there  being 
three  Popes  at  once. 

*  This  eclipse  happened  in  the  first  year  of  the  Pelopon- 
nesian  war. 


Of  Eclipses.  303 

329.  I  have  not  cited  one  half  of  RicciOLUs'sThesuper, 
list  of  portentous  eclipses;  and  for  the  same  reiason^1^ 
that  he  declines  giving  any  more  of  them  than  what  the  anci- 
that  list  contains ;  namely,  that  it  is  most  disagree- 

able  to  dwell  any  longer  on  such  nonsense,  and  a 
much  as  possible  to  avoid  tiring  the  reader:  the 
superstition  of  the  ancients  may  be  seen  by  the  few 
here  copied.  My  author  farther  says,  that  there  were 
treatises  written  to  shew  against  what  regions  the 
malevolent  effects  of  any  particular  eclipse  was  aim- 
ed ;  and  the  writers  affirmed,  that  the  effects  of  an 
eclipse  of  the  Sun  continued  as  many  years  as  the 
eclipse  lasted  hours ;  and  that  of  the  Moon  as  many 
months. 

330.  Yet  such  idle  notions  were  once  of  no  small  Very  for- 
advantage  to  CHRISTOPHER  COLUMBUS,  who,  in^cffor 
the  year  1493,  was  driven  on  the  island  of  Jamaica,  CHRISTO- 
where  he  was  in  the  greatest  distress  for  want  of PHER 

•    •  1  r  i  COLUM- 

provisions,  and  was  moreover  refused  any  assistance  Bus> 
from  the  inhabitants ;  on  which  he  threatened  them 
with  a  plague,  and  told  them,  that  in  token  of  it, 
there  should  be  an  eclipse.  This  accordingly  fell 
on  the  day  he  had  foretold,  and  so  terrified  the  Bar- 
barians, that  they  strove,  who  should  be  first  in 
bringing  him  all  sorts  of  provisions ;  throwing  them 
at  his  feet,  and  imploring  his  forgiveness.  RICCIO- 
i.us's  Almagest,  Vol.  I.  1.  v,  c.  ii. 

331.  Eclipses  of  the  Sun  are  more  frequent  than  Why-there 
those  of  the  Moon,  because  the  Sun's  ecliptic- limits  ^.^)re 
are  greater  than  the  Moon's,  §  317:  yet  we  have  eclipses  of 
more  visible  eclipses  of  the  Moon  than  of  the  Sun,the  Moon 
because  eclipses  of  the  Moon  are  seen  from  all  parts  the'sun, 
of  that  hemisphere  of  the  Earth  which  is  next  her, 

and  are  equally  great  to  each  of  those  parts ;  but  the 
Sun's  eclipses  are  visible  only  to  that  small  portion 
of  the  hemisphere  next  him  whereon  the  Moon's 
shadow  falls,  as  shall  be  explained  by  and  by  at 
large. 

^  332.  The  Moon's  orbit  being  elliptical,  and  the 
Earth  in  one  of  its  focuses,  she  is  once  at  her  least 

Qq 


304  Of  Eclipses. 

Plate  XL  distance  from  the  earth,  and  once  at  her  greatest, 
Fig.  L      in  every  lunation.    When  the  Moon  changes  at  her 
least  distance  from  the  Earth,  and  so  near  the  node 
that  her  dark  shadow  falls  upon  the  Earth,  she  ap- 
pears big  enough  to  cover  the  whole  *  disc  of  the 
Sun  from  that  part  on  which  her  shadow  falls ;  and 
Total  and  the  Sun  appears  totally  eclipsed  there,  as  at  A,  for 
an!mlar    -some  minutes  :  but  when  the  Moon  changes  at  her 

eclipses  of  ,.  ..  .       ,^       ,  , 

the  Sun.  greatest  distance  from  the  Earth,  and  so  near  the 
node  that  her  dark  shadow  is  directed  toward  the 
earth,  her  diameter  subtends  a  less  angle  than  the 
Sun's ;  and  therefore  she  cannot  hide  his  whole  disc 
from  any  part  of  the  Earth,  nor  does  her  shadow 
reach  it  at  that  time ;  and  to  the  place  over  which 
the  point  of  her  shadow  hangs,  the  eclipse  is  annu- 
lar, as  at  B  ;  the  Sun's  edge  appearing  like  a  lumi- 
nous ring  all  around  the  body  of  the  Moon.  When 
the  change  happens  within  17  degrees  of  the  node, 
and  the  Moon  at  her  mean  distance  from  the  Earth, 
the  point  of  her  shadow  just  touches  the  Earth,  and 
she  eclipses  the  Sun  totally  to  that  small  spot  whereon 
her  shadow  falls ;  but  the  darkness  is  not  of  a  mo- 
ment's continuance. 

The  long--      333.  The  Moon's  apparent  diameter,  when  largest, 
estdura-   exceeds  the  Sun's  when  least,  only   1  minute  38 
taTecHp-"  seconds  of  a  degree  :  and  in  the  greatest  eclipse  of 
ses  of  the  the  Sun  that  can  happen  at  any  time  and  place,  the 
total  darkness  continues  no  longer  than  while  the 
Moon  is  going  1  minute  38  seconds  from  the  Sun 
in  her  orbit;  which  is  about  3  minutes  and  13  se- 
conds of  an  hour. 

To  how  334.  The  Moon's  dark  shadow  covers  only  a  spot 
much  of  on  the  Earth's  surface,  about  ISO  English  miles 
the  Surf1  broad,  when  the  Moon's  diameter  appears  largest, 

may  be  to- 
tally or  *  Although  the  Sun  and  Moon  are  spherical  bodies,  as 
eclipsed     seen  *rom  t^ie  ^artn  tney  appear  to  be  circular  planes  ;  and 
at  once       so  WC11M  the  Earth  do.  ii  it  were  seen  from  the  Moon,    i  he 

apparently  flat  surfaces  of  the  Sun  and  Moon  are  called  their 

discs  by  astronomers, 


Of  Eclipses*  305 

and  the  Sun's  least ;  and  the  total  darkness  can  ex-  Plate  XL 
tend  no  farther  than  the  dark  shadow  covers.  Yet 
the  Moon's  partial  shadow  or  penumbra  may  then 
cover  a  circular  space  4900  miles  diameter,  within 
all  which  the  Sun  is  more  or  less  eclipsed,  as  the 
places  are  less  or  more  distant  from  the  centre  of  the 
penumbra.  When  the  Moon  changes  exactly  in  the 
node,  the  penumbra  is  circular  on  the  Earth  at  the 
middle  of  the  general  eclipse ;  because  at  that  time 
it  falls  perpendicularly  on  the  Earth's  surface :  but 
at  every  other  moment  it  falls  obliquely,  and  will 
therefore  be  elliptical,  and  the  more  so,  as  the  time 
is  longer  before  or  after  the  middle  of  the  general 
eclipse;  and  then,  much  greater  portions  of  the 
Earth's  surface  are  involved  in  the  penumbra. 

335.  When  the  penumbra  first  touches  the  Earth,  Duration 
the  general  eclipse  begins :  when  it  leaves  the  Earth,  of  general 
the  general  eclipse  ends :  from  the  beginning  to  the  cuiar  edp- 
end  the  Sun  appears  eclipsed  in  some  part  of  theses. 
Earth  or  other.    When  the  penumbra  touches  any 
place,  the  eclipse  begins  at  that  place,  and  ends  when 

the  penumbra  leaves  it.  When  the  Moon  changes 
in  the  node,  the  penumbra  goes  over  the  centre  of 
the  Earth's  disc  as  seen  from  the  Moon  ;  and  con- 
sequently by  describing  the  longest  line  possible  on 
the  Earth,  continues  the  longest  upon  it;  namely, 
at  a  mean  rate,  5  hours  50  minutes :  more,  if  the 
Moon  be  at  her  greatest  distance  from  the  Earth, 
because  she  then  moves  slowest ;  less,  if  she  be  at 
her  least  distance,  because  of  her  quicker  motion. 

336.  To  make  the  last  five  articles  and  several  Fig.  I/, 
other  phenomena  plainer,  let  S  be  the  Sun,  E  the 
Earth,  M  the  Moon,  and  AMP  the  Moon's  orbit. 
Draw  the  right  line  We  12  from  the  western  side 

of  the  Sun  at  W^  touching  the  western  side  of  the 
Moon  at  c,  and  the  Earth  at  12 :  draw  also  the  right 
line  Vd  12  from  the  eastern  side  of  the  Sun  at  V> 
touching  the  eastern  side  of  the  Moon  at  r/,  and  the 


306  Of  Eclipses. 

The  ^  Earth  at  12 :  the  dark  space  ce  12  d  included  be* 
dariTsha-  tween  those  lines  in  the  Moon's  shadow,  ending  in 
dow,  a  point  at  12,  where  it  touches  the  Earth ;  because 
in  this  case  the  Moon  is  supposed  to  change  at  M 
in  the  middle  between  A  the  apogee,  or  farthest 
point  of  her  orbit  from  the  Earth,  and  P  the  peri- 
gee, or  nearest  point  to  it.  For,  had  die  point  P 
been  at  J/,  the  Moon  had  been  nearer  the  Earth ; 
and  her  dark  shaded  at  e  would  have  covered  a 
space  upon  it  about  180  miles  broad,  and  the  Sun 
would  have  been  totally  darkened,  as  at.//  (Fig.  I,) 
with  some  continuance  :  but  had  the  point  A  (Fig. 
II,)  been  at  J/,  the  Moon  would  have  been  farther 
from  the  Earth,  and  her  shadow  would  have  ended 
in  a  point  about  e,  and  therefore  the  Sun  would  have 
andpe-  appeared,  as  at./?  (Fig.  L),  like  a  luminous  ring  all 
numbra*  around  the  Moon.  Draw  the  right  lines  W '  Xdh 
and  PXcg)  touching  the  contrary  sides  of  the  Sun 
and  Moon,  and  ending  on  the  Earth  at  a  and  b: 
draw  also  the  right  line  S  XM  12,  from  the  centre 
of  the  Sun's  disc,  through  the  Moon's  centre,  to 
the  Earth  at  12 ;  and  suppose  the  two  former  lines 
WXdh  and  VXcg  to  revolve  on  the  line  SXM 
12  as  an  axis,  and  their  points  a  and  b  will  describe 
the  limits  of  the  penumbra  TT  on  the  Earth's  sur- 
face, including  the  large  space  a  0  b  12  a,  within 
which  the  Sun  appears  more  or  less  eclipsed,  as  the 
places  are  more  or  less  distant  from  the  verge  of 
the  penumbra  a  0  b.  t 

Digits,  Draw  the  right  line  y  12  across  the  Sun's  disc, 
what.  perpendicular  to  SXM,  the  axis  of  the  penumbra: 
then  divide  the  line  y  12  into  twelve  equal  parts,  as 
in  the  figure,  for  the  twelve  *  digits  of  the  Sun's 
diameter :  and  at  equal  distances  from  the  centre  of 
the  penumbra  at  12  (on  the  Earth's  surface  YY)  to 
its  edge  a  0  b,  draw  twelve  concentric  circles,  as 
marked  with  the  numeral  figures  1,  2,  3, 4,  &c.  and 

*  A  digit  is  a  twelfth  part  of  the  diameter  of  the  Sun  or 
Moon. 


Of  Eclipses.  307 


remember  that  the  Moon's  motion  in  her  orbit 
A  M  P  is  from  west  to  east,  as  from  s  to  t.    Then, 

To  an  observer  on  the  Earth  at  b,  the  eastern  T 
limb  of  the  Moon  at  d  seems  to  touch  the  western  ™ 
limb  of  the  Sun  at  PF,  when  the  Moon  is  at  M;  eclipse. 
and  the  Sun's  eclipse  begins  at  £,  appearing  as  at 
A  in  Fig,  III,  at  the  left  hand  ;  but  at  the  same 
moment  of  absolute  time  to  an  observer  at  a  in 
Fig.  II,  the  western  edge  of  the  Moon  at  c  leaves 
the  eastern  edge  of  the  Sun  at  F,  and  the  'eclipse 
ends,  as  at  the  right  hand  C  of  Fig.  III.  At  the 
very  same  instant,  to  all  those  who  live  on  the  cir- 
cle marked  1  on  the  Earth  E  in  Fig.  II.  the  Moon 
M  cuts  off  or  darkens  a  twelfth  part  of  the  Sun  5, 
and  eclipses  him  one  digit,  as  at  ]  in  Fig.  Ill  :  to 
those  who  live  on  the  circle  marked  2  in  Fig.  II, 
the  Moon  cuts  off  two  twelfth  parts  of  the  Sun, 
as  at  2  in  Fig.  Ill  :  to  those  on  the  circle  3,  three 
parts;  and  so  on  to  the  centre  at  12  in  Fig.  II, 
where  the  Sun  is  centrally  eclipsed  as  at  B  in  the 
middle  of  Fig.  Ill  ;  under  which  figure  there  is  a 
scale  of  hours  and  minutes,  to  shew,  at  a  mean  rate,  FlS-  n 
how  long  it  is  from  the  beginning  to  the  end  of  a 
central  eclipse  of  the  Sun  on  the  parallel  of  London  ; 
and  how  many  digits  are  eclipsed  at  any  particular 
time  from  the  beginning  at  A  to  the  middle  at  B,  or 
the  end  at  C.  Thus,  in  1  6  minutes  from  the  be- 
ginning, the  Sun  is  two  digits  eclipsed  ;  in  an  hour 
and  five  minutes,  eight  digits;  and  in  an  hour  and 
thirty-seven  minutes,  12  digits. 

337.  By  Fig.  II,  it  is  plain,  that  the  Sun  is  total-  FL 
ly  or  centrally  eclipsed  but  to  a  small  part  of  the 
Earth  at  any  time  ;  because  the  dark  conical  shadow 
e  of  the  Moon  M  falls  but  on  a  small  part  of  the 
Earth  :  and  that  a  partial  eclipse  is  confined  at  that 
time  to  the  space  included  by  the  circle  a  0  £,  c: 
which  only  one  half  can  be  projected  in  the  figure, 
the  other  half  being  supposed  to  be  hid  by  the  con- 
vexity of  the  Earth  E  ;  and  likewise,  that  no  parr 


308  Of  Eclipse*. 

Plats  XL  of  the  Sun  is  eclipsed  to  the  large  space  TT  of  the 
Earth,  because  the  Moon  is  not  between  the  Sun  and 
cit%Ttheany      thatpart  of  the  Earth:  and  therefore  to  all  that 
Moon's  iepart  the  eclipse  is  invisible.     The  Earth  turns  east* 
shadow  on  warcj  on  its  axis,  as  from  g  to  /;?,  which  is  the  same 
lt  way  that  the  Moon's  shadow  moves;  but  the  Moon's 
motion  is  much  swifter  in  her  orbit  from  s  to  /  :  and 
therefore,  although  eclipses  of  the  Sun  are  of  longer 
duration  on  account  of  the  Earth's  motion  on  its 
axis  than  they  would  be  if  that  motion  was  stopt,  yet 
in  four  minutes  of  time  at  most  the  Moon's  swifter 
motion  carries  her  dark  shadow  quite  over  any  place 
that  its  centre  touches  at  the  time  of  greatest  obscu- 
ration. The  motion  of  the  shadow  on  the  Earth's  disc 
is  equal  to  the  Moon's  motion  from  the  Sun,  which 
is  about  30-^  minutes  of  a  degree  every  hour  at  a 
mean  rate;  but  so  much  of  the  Moon's  orbit  is  equal 
to  SO-  degrees  of  a  great  circle  on  the  Earth,  §  32O; 
and  therefore  the  Moon's  shadow  goes  30-  degrees 
or  1 830  geographical  miles  on  the  Earth  in  an  hour, 
or  30]  miles  in  a  minute,  which  is  almost  four  times 
as  swift  as  the  motion  of  a  cannon  ball. 
Figr-  iv.         338.  As  seen  from  the  Sun  or  Moon,  the  Earth's 
axis  appears  differently  inclined  every  day  of  the  year, 
on  account  of  keeping  its  parallelism  throughout  its 
annual  course.    Let  £,  D,  0,  N9  be  the  Earth  at  the 
two  equinoxes,  and  the  two  solstices,  NS  its  axis,  N 
the  north  pole,  5  the  south  pole,  JE  Q  the  equator, 
T  the  tropic  of  Cancer,  t  the  tropic  of  Capricorn, 
and  ABC  the  circumference  of  the  Earth's  enlight- 
ened disc  as  seen  from  the  Sun  or  new  Moon  at  these 
Phenome.  times.  The  Earth's  axis  has  the  position  N E  S  at 
Earti^as6  t^le  verna^  equinox,  lying  toward  the  right  hand,  as 
seen  from  seen  from  the  Sun  or  new  Moon  ;  its  poles  A' and  S 
the  sunol*beimr  then  in  the  circumference  of  the  disc  ;  and  the 

new  Moon  o  •    i      i- 

atdifferent  equator  and  all  its  parallels  seem  to  be  straight  lines, 

times  of    because  their  planes  pass  through  the  observer's  eye 

looking  down  upon  the  Earth  from  the  Sun  or  Moon 

directly  over  E,  where  the  ecliptic  F G  intersects  the 


Of  Eclipses.  309 

equator  JE  Q.->  At  the  summer  solstice,  the  Earth's 
axis  has  the  position  NDS;  and  that  part  of  the  eclip- 
tic FG,  in  which  the  Moon  is  then  new,  touches  the 
tropic  of  Cancer  T  at  D.  The  north  pole  N  at  that 
time  inclining  23 *  degrees  toward  the  Sun,  falls  so  ' 
many  degrees  within  the  Earth's  enlightened  disc; 
because  the  Sun  is  then  vertical  to  Z),  23V  degrees 
north  of  the  equator  M  Q;  and  the  equator,  with  all 
its  parallels  seem  elliptic  curves  bending  downward, 
or  toward  the  south  pole,  as  seen  from  the  Sun: 
which  pole,  together  with  237  degrees  all  round  it, 
is  hid  behind  the  disc  in  the  dark  hemisphere  of  the 
Earth.  At  the  autumnal  equinox,  the  Earth's  axis 
has  the  position  NOS9  lying  to  the  left  hand  as  seen 
from  the  Sun  or  new  Moon,  which  are  then  vertical 
to  0,  where  the  ecliptic  cuts  the  equator  £  O.  Both 
poles  now  lie  in  the  circumference  of  the  disc,  the 
north  pole  just  going  to  disappear  behind  it,  and  the 
south  pole  just  entering  into  it ;  and  the  equator  with 
all  its  parallels  seem  to  be  straight  lines,  because  their 
planes  pass  through  the  observer's  eye,  as  seen  from 
the  Sun,  and  very  nearly  so  as  seen  from  the  Moon. 
At  the  winter  solstice,  the  Earth's  axis  has  the  position 
NNS  ;  when  its  south  pole  S  inclining  23J  degrees 
towards  the  Sun,  falls  23  degrees  within  the  enlight- 
ened disc,  as  seen  from  the  Sun  or  new  Moon,  which 
are  then  vertical  to  the  tropic  of  Capricorn  /,  23]  de- 
grees south  of  the  equator  JE  O;  and  the  equator  with 
all  its  parallels  seem  elliptic  curves  bending  upward  ; 
the  north  pole  being  as  far  behind  the  disc  in  the 
dark  hemisphere,  as  the  south  pole  is  come  into  the 
light.  The  nearer  that  any  time  of  the  year  is  to 
the  equinoxes  or  solstices,  the  more  it  partakes  of  the 
phenomena  relating  to  them. 

339.  Thus  it  appears,  that  from  the  vernal  equi- 
nox to  the  autumnal,  the  north  pole  is  enlightened  ; 
and  the  equator  and  all  its  parallels  appear  elliptical 
as  seen  trom  the  Sun,  more  or  less  curved  as  the 
time  is  pearer  to  or  farther  from  the  summer  sol- 


310  Of  Eclipses. 

Plate  XL  st|ce  .  and  bending  downward,  or  toward  the  south 

Var-.pis     pole;  the  reverse  of  which  happens  from   the  au- 

ofthe'™'   tumnal  equinox  to  the  vernal.    A  little  consideration 

Earth's     will  be  sufficient  to  convince  the  reader,  that  the 

teeiifVom  ^artn's  ax*s  inclines  toward  the  Sun  at  the  summer 

the  Sun  at  solstice  ;  f  rom  the  Sun  at  the  winter  solstice  ;   and 

tlme^'of-    sidewise  to  the  Sun  at  the  equinoxes ;  but  toward 

the  year,    the  right  hand,  as  seen  from  the  Sun  at  the  vernal 

equinox  ;  and  toward  the  left  hand  at  the  autumnal, 

From  the  winter  to  the  summer  solstice,  the  Earth's 

'axis  inclines  more  or  less  to  the  right  hand,  as  seen 

from  the  Sun  ;  and  the  contrary  from  the  summer: 

to  the  winter  solstice. 

jfow  these      340.  The  different  positions  of  the  Earth's  axis, 
affect  solar as  seen  ^rom  tne  ^un  at  different  times  of  the  year, 
eclipses,    affect  solar  eclipses  greatly  with  regard  to  particular 
places ;  yea  so  far  as  would  make  central  eclipses 
which  fall  at  one  time  of  the  year,  invisible  if  they 
had  fallen  at  another  ;  even  though' the  Moon  should 
always  change  in  the  nodes,  and  at  the  same  hour  of 
the  day :  of  which  indefinitely  various  affections,  we 
shall  only  give  examples  for  the  times  of  the  equi- 
noxes and  solstices. 

Fig.  iv.  In  the  same  diagram,  let  FG  be  part  of  the  eclip- 
tic, and  IK,  i  k,  i  k,  i  k,  part  of  the  Moon's  orbit ; 
both  seen  edgewise,  and  therefore  projected  into  right 
lines ;  and  let  the  intersections  TV,  0,  £),  £,  be  one 
and  the  same  nodes  at  the  above  times,  when  the 
Earth  has  the  forementioned  different  positions;  and 
let  the  space  included  by  the  circles,  P,  /,  p,  p,  be 
the  penumbra  at  these  times,  as  its  centre  is  passing 
over  the  centre  of  the  Earth's  disc.  At  the  winter 
solstice,  when  the  Earth's  axis  has  the  position 
N  N  6\  the  centre  of  the  penumbra  P  touches  the 
tropic  of  Capricorn  /  in  N  at  the  middle  of  the  ge- 
neral eclipse  ;  but  no  part  of  the  penumbra  touches 
the  tropic  of  Cancer  T.  At  the  summer  solstice, 
when'the  Earth's  axis  has  the  position  ND  S  (i  D  k 


Of  Eclipses. 

being  then  part  of  the  Moon's  orbit,  whose  node  is 
at  Z)),  the  penumbra  p  has  its  centre  at  I),  on  the 
tropic  of  Cancer  T9  at  the  middle  of  the  general 
eclipse,  and  then  no  part  of  it  touches  the  tropic  of 
Capricorn  /.  At  the  autumnal  equinox,  the  Earth's 
axis  has  the  position  N  0  S  (i  0  k  being  then  part 
of  the  Moon's  orbit),  and  the  penumbra  equally  in- 
eludes  part  of  both  tropics  7" and  t  at  the  middle  of 
the  general  eclipse :  at  the  vernal  equinox  it  does 
the  same,  because  the  Earth's  axis  has  the  position 
N E  S :  but  in  the  former  of  these  two  last  cases, 
the  penumbra  enters  the  Earth  at  A,  north  of  the 
tropic  of  Cancer  T,  and  leaves  ii  at  m,  south  of  the 
tropic  of  Capricorn  /;  having  gone  over  the  Earth 
obliquely  southward,  as  its  centre  described  the  line 
AOm:  whereas,  in  the  latter  case,  the  penumbra 
touches  the  Earth  at  ;;,  south  of  the  equator  JE  6>, 
and  describing  the  line  n  E  q  (similar  to  the  former 
line  AOm  in  open  space)  goes  obliquely  northward 
over  the  earth,  and  leaves  it  at  ^,  north  of  the  equa- 
tor. 

In  all  these  circumstances,  the  Moon  has  been 
supposed  to  change  at  noon  in  her  descending  node : 
had  she  changed  in  her  ascending  node,  the  pheno- 
mena would  have  been  as  various  the  contrary  way, 
with  respect  to  the  penumbra's  going  northward  or 
southward  over  the  Earth.  But  because  the  Moon 
changes  at  all  hours,  as  often  in  one  node  as  in  the 
other,  and  at  all  distances  from  them  both  at  differ- 
ent times  as  it  happens,  the  variety  of  the  phases  of 
eclipses  are  almost  innumerable,  even  at  the  same 
places;  especially  considering  how  variouslv  the 
same  places  are  situate  on  the  enlightened  disc  of  the 
Earth,  with  respect  to  the  penumbra's  motion,  at  the 
different  hours  when  eclipses  happen. 

341.  When  the  Moon  changes  17  degrees  short  HOW 
of  her  descending  node,  the  penumbra  P  \  8  just  |n.;1(,he('' 

touches  the  northern  part  of  the  Earth's  disc,  near  uumbr* 

i)  j.  folia  MI  tW 


Of  Eclipses. 


distances  Moon  appears  to  touch  the  Sun,  but  hides  no  part 

fco°desthe  °^  kim  *rom  ^g^  ^ac*  tne  change  been  as  far 
short  of  the  ascending  node  ;  the  penumbra  would 
have  touched  the  southern  part  of  the  disc  near  the 
south  pole  S.  When  the  Moon  changes  12  degrees 
short  of  the  descending  node,  more  than  a  third  part 
of  the  penumbra  P  1  2  falls  on  the  northern  parts  of 
the  Earth  at  the  middle  of  the  general  eclipse  :  had 
she  changed  as  far  past  the  same  node,  as  much  on 
the  other  side  of  the  penumbra  about  P  would  have 
fallen  on  the  southern  part  of  the  Earth  ;  all  the  rest 
in  the  expansion  or  open  space.  When  the  Moon 
changes  6  degrees  from  the  node,  almost  the  whole 
penumbra  P  6  falls  on  the  Earth  at  the  middle  of  the 
general  eclipse.  And  lastly,  when  theMoon  changes 
in  the  node  at  A7,  the  penumbra  P  N  takes  the  long- 
est  course  possible  on  the  Earth's  disc  ;  its  centre 
falling  on  the  middle  of  it,  at  the  middle  of  the  ge- 
neral eclipse.  The  farther  the  Moon  changes  from 
either  node,  within  1  7  degrees  of  it,  the  shorter  is 
the  penumbra's  continuance  on  the  Earth,  because 
it  goes  over  a  less  proportion  of  the  disc,  as  is  evi- 
dent by  the  figure. 

Earth's          342>  T^e  nearer  tnat  tne  penumbra's  centre  is  to 

diumai     the  equator  at  the  middle  of  the  general  eclipse,  the 

lengthens  ^onger  *s  tne  duration  of  the  eclipse  at  all  those 

the  dura-  places  where  it  is  central  ;  because,  the  nearer  that 

hrecfi  *°~  *ny  P*ace  ^  to  t^le  equator  the  greater  is  the  circle 

ses,  which  it  describes  by  the  Earth's  motion  on  its  axis  ;  and 

mltthe^o  s°5  t^ie  P^ace  m°ving  quicker,  keeps  longer  in  the 

tar  circles,  penumbra,  whose  motion  is  the  same  way  with  that 

of  the  place,  though  faster,  as  has  been  already 

mentioned,  §  337.    Thus  (see  the  Earth  at  D  and 

the  penumbra  at  12)  while  the  point  b  in  the  polar 

circle  a  b  c  d  is  carried  from  b  to  c  by  the  Earth's 

diurnal  motion,  the  point  d  on  the  tropic  of  Cancer 

T  is  carried  a  much  greater  length  from  d  to  D  : 


Of  Eclipses. 

and  therefore,  if  the  penumbra's  centre  should  go  one 
time  over  c,  and  another  time  over  D,  the  penumbra 
will  be  longer  in  passing  over  the  moving-place  d, 
than  it  was  in  passing  over  the  moving-place  b.  Con- 
sequently, central  eclipses  about  the  poles  are  of  the 
shortest  duration ;  and  about  the  equator  of  the 
longest. 

343.  In  the  middle  of  summer,  the  whole  frigid 

....        .  .17        7  •          v    i       ens  the  du- 

zone,  included  by  the  polar  circle  ab  <:<:/,  is  enhght-  ration  of 
ened  ;  and  if  it  then  happens  that  the  penumbra's  »°™* 
centre  passes  over  the  north  pole,  the  Sun  will  be  within  * 
eclipsed  much  the  same  number  of  digits  at  a  as  at these  c!*- 
c  ;  but  while  the  penumbra  moves  eastward  over  r/  ' 
it  moves  westward  over  a9  because,  with  respect  to 
the  penumbra,  the  motions  of  a  and  c  are  contrary: 
for  c  moves  the  same  way  with  the  penumbra  toward 
d,  but  a  moves  the  contrary  way  toward  b;  and  there- 
fore  the  eclipse  will  be  of  longer  duration  at  c  than 
at  a.    At  a,  the  eclipse  begins  on  the  Sun's  eastern 
limb,  but  at  <:,  on  his  western :  at  all  places  lying 
without  the  polar  circles,  the  Sun's  eclipses  begin 
on  his  western  limb,  or  near  it,  and  end  on  or  near 
his  eastern.    At  those  places  where  the  penumbra 
touches  the  earth,  the  eclipse  begins  with  the  rising 
Sun,  on  the  top  of  his  western  or  uppermost  edge; 
and  at  those  places  where  the  penumbra  leaves  the 
Earth,  the  eclipse  ends  with  the  setting  Sun,  on  the 
top  of  his  eastern  edge,  which  is  then  the  uppermost, 
just  at  its  disappearing  on  the  liorizon. 
344.IftheMoonweresurroundedbyanatmosphereTbeMoof> 

of  any  considerable  density,  it  would  seem  to  touch 
the  Sun  a  little  before  the  Moon  made  her  appulse 
to  his  edge,  and  we  should  see  a  little  faintness  on 
that  edge  before  it  was  eclipsed  by  the  Moon:  but 
as  no  such  faintness  has  been  observed,  at  least  so 
far  as  I  have  ever  heard,  it  seems  plain,  that  the 
Moon  has  no  such  atmosphere  as  that  of  the  Earth. 
The  faint  ring  of  light  surrounding  the  Sun  in  to- 


314  Of  Eclipses. 

Plate  XL  tal  eclipses,  called  by  CASSINI  la  Chevelure  du 
Sohil,  seems  to  be  the  atmosphere  of  the  Sun  ;  be- 
cause it  has  been  observed  to  move  equally  with  the 
Sun,  not  with  the  Moon. 

345.  Having  said  so  much  about  eclipses  of  the 
Sun,  we  shall  drop  that  subject  at  present,  and  pro- 
ceed to  the  doctrine  of  lunar  eclipses:  which,  being 
more  simple,  may  be  explained  in  less  time. 

fte 'Moon'f  ^  ^at  tne  Moon  can  never  be  eclipsed  but  at  the 
time  of  her  being  full,  and  the  reason  why  she  is 
not  eclipsed  at  every  full,  has  been  shewn  already. 

Fig.  ii.  §  3)6,  317.  Let  S  be  the  Sun,  E  the  Earth,  RR 
the  Earth's  shadow,  and  B  the  Moon  in  opposition 
to  the  Sun  :  in  this  situation  the  Earth  intercepts 
the  Sun's  light  in  its  way  to  the  Moon :  and  when 
the  Moon  touches  the  Earth's  shadow  at  v,  she  be- 
gins to  be  eclipsed  on  her  eastern  limb  #,  and  con- 
tinues eclipsed  until  her  western  limb  y  leaves  the 
shadow  at  iv;  at  B  she  is  in  the  middle  of  the 
shadow,  and  consequently  in  the  middle  of  the 
eclipse. 

346.  The  Moon  when  totally  eclipsed  is  not  in- 
visible, if  she  be  above  the  horizon,  and  the  sky  be 
clear  ;  but  appears  generally  of  a  dusky  colour  like 
tarnished  copper,  which  some  have  thought  to  be 

why  the  the  Moon's  native  light.    But  the  true  cause  of  her 
Moon  is    bempp  visible  is  the  scattered  beams  of  the  Sun,  bent 

visible  in  a .          P.      „        ,  ,      ,  .  ,     , 

total  into  the  Earth  s  shadow  by  going  through  the  atmos- 
«?ciipse.  phere;  which, being  more  dense  near  the  Earth  than 
at  considerable  heights  above  it,  refracts  or  bends 
theSun's  rays  more  inward,  §  179;  and  those  which 
pass  nearest  the  Earth's  surface,  are  bent  more  than 
those  rays  which  go  through  higher  parts  of  the  at- 
mosphere, where  it  is  less  dense,  until  it  be  so  thin 
or  rare  as  to  lose  its  refractive  power.  Let  the 
circle  fg  h  /,  concentric  to  the  Earth,  include  the 
atmosphere,  whose  refractive  power  vanishes  at  the 
heights /and  /';  so  that  the  rays  W fw  and  Vi  v 


Of  Eclipses.  31.5 

go  on  straight  without  suffering  the  least  refraction.  Ptat*  XL 
But  all  those  rays  which  enter  the  atmosphere,  be- 
tween f  and  £,  and  between  /  and  /,  on  opposite 
sides  of  the  Earth,  are  gradually  more  bent  inward  as 
they  go  through  a  greater  portion  of  the  atmosphere, 
until  the  rays  W  k  and  V I  touching  the  Earth  at  m 
and  ?2,  are  bent  so  much  as  to  meet  at  q,  a  little 
short  of  the  Moon  ;  and  therefore  the  dark  shadow 
of  the  Earth  is  contained  in  the  space  m  o  q  p  ??, 
where  none  of  the  Sun's  rays  can  enter  :  all  the  rest 
R  R,  being  mixed  by  the  scattered  rays  which  are 
refracted  as  above,  is  in  some  measure  enlightened 
by  them ;  and  some  of  those  rays  falling  on  the 
Moon,  give  her  the  colour  of  tarnished  copper,  or 
of  iron  almost  red-hot.  So  that  if  the  Earth  had  no 
atmosphere,  the  Moon  would  be  as  invisible  in  to- 
tal eclipses  as  she  is  when  new.  If  the  Moon  were 
so  near  the  Earth  as  to  go  into  its  dark  shadow,  sup- 
pose about  p  o,  she  would  be  invisible  during  her 
stay  in  it ;  but  visible  before  and  after  in  the  fainter 
shadow  R  R. 

347,  When  the  Moon  goes  through  the  centre  of  why  the 
the  Earth's  shadow,  she  is  directly   opposite ,  to  the  ,;'^'"j.e 
Sun  :  yet  the  Moon  has  been  often  seen  totally  eclips-  sometimes 
ed  in  the  horizon  when  the  Sun  was  also  visible  i 

the  opposite  part  of  it :  for,  the  horizontal  refraction  MOOU 
being  almost  34  minutes  of  a  degree,  §181,  and  the 
diameter  of  the  Sun  and  Moon  being  each  at  a  mean 
state  but  32  minutes,  the  refraction  causes  both  lu- 
minaries to  appear  above  the  horizon  when  they  are 
really  below  it,  §  1 79. 

348.  When  the  Moon  is  full  at  12  degrees  from 
either  of  her  nodes,  she  just  touches  the  Earth's  sha- 
dow, but  enters  not  into  it.     Let  G  H  be  the  eclip- 
tic, ef  the  Moon's  orbit  where  she  is    12   degrees 
from  the  node  at  her  full ;  c  d  her  orbit  where  she  is 
6  degrees  from  the  node;  a  b  her  orbit  where  she  is 
full  in  the  node;  A  B  the  Earth's  shadow,  and  M 


516  Of  Eclipses. 

Duration  the  Moon.  When  the  Moon  describes  the  line  efy 
ccH^sesoV  S^e  Just  toucnes  tne  shadow,  but  does  not  enter  into 
the  Moon,  it  ;  when  she  describes  the  line  c  d,  she  is  totally, 
though  not  centrally  immersed  in  the  shadow  ;  and 
when  she  describes  the  line  a  b,  she  passes  by  the 
node  at  M  in  the  centre  of  the  shadow  ;  and  takes 
the  longest  line  possible,  which  is  a  diameter,  through 
it:  and  such  an  eclipse  being  both  total  and  central 
is  of  the  longest  duration,  namely,  3  hours  57  mi- 
nutes 6  seconds  from  the  beginning  to  the  end,  if 
the  Moon  be  at  her  greatest  distance  from  the  Earth; 
and  3  hours  37  minutes  26  seconds,  if  she  be  at 
her  least  distance.  The  reason  of  this  difference 
is,  that  when  the  Moon  is  farthest  from  the  Earth, 
she  moves  the  slowest  ;  and  when  nearest  to  it,  the 
quickest. 

Digits.          349.  The  Moon's  diameter,  as  well  as  the  Sun's, 

is  supposed  to  be  divided  into  twelve  equal  parts, 

called  digits  ;  and  so  many  of  these  parts  as  are 

darkened  by  the  Earth's  shadow,  so  many  digits  is 

the  Moon  eclipsed.     All  that  the  Moon  is  eclipsed 

above  12  digits,  shew,  how  far  the  shadow  of  the 

Earth  is  over  the  body  of  the  Moon,  on  that  edge 

to  which  she  is  nearest  at  the  middle  of  the  eclipse. 

why  the        350.  It  is  difficult  to  observe  exactly  either  the 

anTendof  Beginning  or  ending  of  a  lunar  eclipse,  even  with  a 

a  lunar      good  telescope  ;  because  the  Earth's  shadow  is  so 

?cliPs°      faint  and  ill-defined  about  the  edges,  that  when  the 

is  so  tlifa-  ^  .  .  •         •         1         i 

cult  to  be  Moon  is  either  just  touching  or  leaving  it,  the  ob- 
1"  scurati°n  °*'  k£r  *irnb  *s  scarce  sensible  ;  and  there- 


aervation"  fore  the  nicest  observers  can  hardly  be  certain  to  se- 
veral seconds  of  time.  But  both  the  beginning  and 
ending  of  solar  eclipses  are  visibly  instantaneous  : 
for  the  moment  that  the  edge  of  the  Moon's  disc 
touches  the  Sun's,  his  roundness  seems  a  little  broken 
on  that  part  ;  and  the  moment  she  leaves  it,  he  ap- 
pears perfectly  round  again. 

The  use  of     351.  In  astronomy,  eclipses  of  the  Moon  are  of 
fn'llrtro-    great  use  for  ascertaining  the  periods  of  her  motions  ; 

no  my, 


Of  Eclipses.  317 


especially  such  eclipses  as  are  observed  to  be  alike  i 
ull  circumstances,  and  have  long  intervals  of  ti 
between  them.  In  geography,  the  longitudes 
places  are  found  by  eclipses,  as  already  shewn  in  the 
eleventh  chapter.  In  chronology,  both  solar  and  lu- 
nar eclipses  serve  to  determine  exactly  the  time  of 
any  past  event:  for  there  are  so  many  particulars  ob- 
servable in  every  eclipse,  with  respect  to  its  quanti- 
ty, the  places  where  it  is  visible  (if  of  the  Sun,)  and 
the  time  of  the  day  or  night  ;  that  it  is  impossible 
there  can  be  two  solar  eclipses  in  the  course  of  ma- 
ny ages  which  are  alike  in  all  circumstances. 

352.  From  the  above  explanation  of  the  doctrine  The  dkrk- 
of  eclipses,  it  is  evident  that  the  darkness  at  our  SA-"urSsaA. 
VIOUR'S  crucifixion  was  supernatural.     For  he  suf-  VJOUR'S 
fered  on  the  day  on  which  the  passover  was  eaten  by 
the  Jews,  on  which  day  it  was  impossible  that 
Moon's  shadow  could  fall  on  the  Earth;  for  the  Jews 
kept  the  passover  at  the  time  of  full  Moon:  nor  does 
the  darkness  in  total  eclipses  of  the  Sun  last   above 
four  minutes  in  any  place,  §  333,  whereas  the  dark- 
ness at  the  crucifixion  lasted  three  hours,  Matt. 
xxviii.  15.  and  overspread  at  least  all  the  land  of 
Judea. 


The  Construction  of  the  following  Tables* 


CHAP.  XIX. 

Shewing  the  Principles  on  which  the  following  Astro- 
nomical Tables  are  constructed,  and  the  Method  of 
co.  I  dilating  the  Times  of  New  and  Full  Moons  and 
Eclipses  by  them. 


353  nearer  that  any  object  is  to  the  eye  of 

JL    an  observer,  the  greater  is  the  angle  un- 
der which  it  appears  :  the  farther  from  the  eye,  the  less. 

The  diameters  of  the  Sun  and  Moon  subtend  dif- 
ferent angles  at  different  times.  And  at  equal  in- 
tervals of  time,  these  angles  are  once  at  the  greatest, 
and  once  at  the  least,  in  somewhat  more  than  a  com- 
plete revolution  of  the  luminary  through  the  eclip- 
tic, from  any  given  fixed  star  to  the  same  star 
again.  —  This  proves  that  the  Sun  and  Moon  are 
constantly  changing  their  distances  from  the  Earth  ; 
and  that  they  are  once  at  their  greatest  distance  and 
once  at  their  least,  in  little  more  than  a  complete  re- 
volution. 

The  gradual  differences  of  these  angles  are  not 
what  they  would  be,  if  the  luminaries  moved  in 
circular  orbits,  the  Earth  being  supposed  to  be 
placed  at  some  distance  from  the  centre  :  but  they 
agree  perfectly  with  elliptic  orbits,  supposing  the  low- 
er focus  of  each  orbit  to  be  at  thecentre  of  the  Earth.* 

The  farthest  point  of  each  orbit  from  the  Earth's 
centre  is  called  the  apogee,  and  the  nearest  point  is 
called  the  perigee.  —  These  points  are  directly  oppo- 
site to  each  other. 

Astronomers  divide  each  orbit  into  12  equal  parts 
called  signs  ;  each  sign  into  SO  equal  parts,  called 
degrees  ;  each  degree  into  60  equal  parts,  called  mi- 
nutes ;  and  every  minute  into  60  equal  parts,  called 
seconds.  The  distance  of  the  Sun  or  Moon  from 

*  The  Sun  is  in  the  focus  of  the  Earth's  orbit,  and  the 
Earth  in  or  near  that  of  the  Moon's  orbit. 


The  Construction  of  the  following  Tables.  519 

any  given  point  of  its  orbit,  is  reckoned  in  signs, 
degrees,  minutes,  and  seconds.  Here  we  mean  the 
distance  that  the  luminary  has  moved  through  from 
any  given  point ;  not  the  space  it  is  short  of  it  in 
coming  round  again,  though  ever  so  little. 

The  distance  of  the  Sun  or  Moon  from  its  apo- 
gee at  any  given  time  is  called  its  mean  anomaly  : 
so  that,  in  the  apogee,  the  anomaly  is  nothing ;  in 
the  perigee,  it  is  six  signs. 

The  motions  of  the  Sun  and  Moon  are  observed 
to  be  continually  accelerated  from  the  apogee  to  the 
perigee,  and  as  gradually  retarded  from  the  perigee 
to  the  apogee ;  being  slowest  of  all  when  the  mean 
anomaly  is  nothing,  and  swiftest  of  all  when  it  is 
six  signs. 

When  the  luminary  is  in  its  apogee  or  its  perigee, 
its  place  is  the  same  as  it  would  be,  if  its  motion 
were  equable  in  all  parts  of  its  orbit. — The  sup- 
posed equable  motions  are  called  mean  ;  the  unequa- 
ble are  jusfry  called  the  true . 

The  mean  place  of  the  Sun  or  Moon  is  always  for- 
warder than  the  true  place*,  while  the  luminary  is 
moving  from  its  apogee  to  its  perigee;  and  the  true 
place  is  always  forwarder  than  the  mean,  while  the 
luminary  is  moving  from  its  perigee  to  its  apogee. — 
In  the  former  case,  the  anomaly  is  always  less  than 
six  signs ;  and  in  the  latter  case,  more. 

It  has  been  found,  by  a  long  series  of  observa- 
tions, that  the  Sun  goes  through  the  ecliptic,  from 
the  vernal  equinox  to  the  same  equinox  again,  in 
365  days  5  hours  48  minutes  55  seconds :  from  the 
first  star  of  Aries  to  the  same  star  again,  in  365  days 
6  hours  9  minutes  24  seconds:  and  from  his  apogee 
to  the  same  again,  in  365  days  6  hours  14  minutes 
0  seconds. — The  first  of  these  is  called  the  solar 

*  The  point  of  the  ecliptic  in  which  the  Sun  or  Moon  is  at  any 
given  moment  of  time  is  called  \hefilace  of  the  Sun  or  Moon  at 
that  time. 

S  s 


The-  Construction  of  lhc  following  Tables. 

ijcar>  the  second  the  sidereal  year,  and  the  third  the 
anomalistic  year.  So  that  the  solar  year  is  20  minutes 
29  seconds  shorter  than  the  sidereal;  and  the  sidereal 
year  is  4  minutes  36  seconds  shorter  than  the  ano- 
malistic.— Hence  it  appears  that  the  equinoctial 
point,  or  intersection  if  the  ecliptic  and  equator  at 
the  beginning  of  Aries,  goes  backward  with  respect 
to  the  fixed  stars,  and  that  the  Sun's  apogee  goes 
forward. 

It  is  also  observed,  that  the  Moon  goes  through 
her  orbit  from  any  given  fixed  star  to  the  same  star 
again,  in  27  days  7  hours  43  minutes  4  seconds  at 
a  mean  rate  :  from  her  apogee  to  her  apogee  again, 
in  27  days  13  hours  18  minutes  43  seconds:  and 
from  the  Sun  to  the  Sun  again,  in  29  days  12  hours 
44  minutes  3-fs  seconds.  This  shews,  that  the  Moon's 
apogee  moves  forward  in  the  ecliptic,  and  that  at  a 
much  quicker  rate  than  the  Sun's  apogee  does; 
since  the  Moon  is  5  hours  55  minutes  39  seconds 
longer  in  revolving  from  her  apogee  to  her  apogee 
again,  than  from  any  star  to  the  same  star  again. 

The  Moon's  orbit  crosses  the  ecliptic  in  two  op- 
posite points,  which  are  called  her  nodes :  and  it  is 
observed  that  she  revolves  sooner  from  any  node  to 
the  same  node  again,  than  from  any  star  to  the  same 
star  again,  by  2  hours  38  minutes  27  seconds;  which 
shews  that  her  nodes  move  backward,  or  contrary 
to  the  order  of  signs,  in  the  ecliptic. 

The  time  in  which  the  Moon  revolves  from  the 
Sun  to  the  Sun  again  (or  from  change  to  change)  is 
called  a  lunation\  which,  according  to  Dr.  POUND'S 
mean  measures,  would  always  consist  of  29  days  12 
hours  44  minutes  3  seconds  2  thirds  58  fourths,  if 
the  motions  of  the  Sun  and  Moon  were  always  equa- 
ble*.— Hence,  12  mean  lunations  contain  354  days 

*  We  have  thought  proper  to  keep  by  Dr.  Pound's  length  of  a 
mean  lunation,  because  his  numbers  come  nearer  to  the  times  of  the 
ancient  eclipsesj  than  Mayer's  do,  without  allowing  for  the  Moon% 
acceleration* 


The  Construction  of  the  following  Tables.  321 

3  hours  48  minutes  36  seconds  3 5  thirds  40  fourths, 
which  is  10  days  21  hours  11  minutes  23  seconds 
24  thirds  20  fourths  less  than  the  length  of  a  com- 
mon Julian  year,  consisting  of  365  days  6  hours ; 
and  13  mean  lunations  contain  383  days  21  hours 
32  minutes  39  seconds  38  thirds  38  fourths,  which 
exceeds  the  length  of  a  common  Julian  year,  by  18 
days  15  hours  32  minutes  39  seconds  38  thirds  38 
fourths. 

The  mean  time  of  new  Moon  being  found  for  any 
given  year  and  month,  as  suppose  for  March  1700, 
old  style,  if  this  mean  new  Moon  falls  later  than  the 
llth  day  of  March,  then  12  mean  lunations,  added 
to  the  time  of  this  mean  new  Moon,  will  give  the 
time  of  the  mean  new  Moon  in  March  1701,  after 
having  thrown  off  365  days. — But  when  the  mean 
new  Moon  happens  to  be  before  the  llth  of  March, 
we  must  add  13  mean  lunations,  in  order  to  have 
the  time  of  mean  new  Moon  in  March  the  year  fol- 
lowing ;  always  taking  care  to  subtract  365  day  sin 
common  years,  and  366  days  in  leap-years,  from 
the  sum  of  this  addition. 

Thus,  A.  D.  1700,  old  style,  the  time  of  mean 
new  Moon  in  March,  was  the  8th  day,  at  16  hours 
11  minutes  25  seconds  after  the  noon  of  that  day 
(viz.  at  11  minutes  25  seconds  past  IV  in  the  morn- 
ing of  the  9th  day,  according  to  common  reckon- 
ing). To  this  we  must  add  13  mean  lunations,  or 
383  days  21  hours  32  minutes  39  seconds  38  thirds 
38  fourths,  and  the  sum  will  be  392  days  13  hours 
44  minutes  4  seconds  38  thirds  3 8  fourths;  from 
which  subtract  365  days,  because  the  year  1701 
is  a  common  year,  and  there  will  remain  27  days 
13  hours  44  minutes  4  seconds  38  thirds  38  fourths 
for  the  time  of  mean  new  Moon  in  March,  A.  D. 
1701. 

Carrying  on  this  addition  and  subtraction  till 
A.  D.  1703,  we  find  the  time  of  mean  new  Moon 
in  March  that  year,  to  be  on  the  6th  day  at  7  hours 


322  The  Construction  of  the  following  Tables. 

21  minutes  17  seconds  49  thirds  46  fourths  past 
noon ;  to  which  add  13  mean  lunations,  and  the  sum 
will  be  390  days  4  hours  53  minutes  57  seconds  28 
thirds  20  fourths  ;  from  which  subtract  366  days, 
because  the  year  ]  704  is  a  leap-year,  and  there  will 
remain  24  days  4  hours  53  minutes  57  seconds  28 
thirds  20  fourths  for  the  time  of  mean  new  Moon  in 
March,  A.  D.  1704. 

In  this  manner  was  the  first  of  the  following  tables 
constructed  to  seconds,  thirds,  arid  fourths;  and  then 
written  out  to  the  nearest  second. — The  reason  why 
we  chose  to  begin  the  year  with  March*  was  to  avoid 
the  inconvenience  of  adding  a  day  to  the  tabular  time 
in  leap-years  after  February,  or  subtracting  a  day 
therefrom  in  January  and  February  in  those  years  ; 
to  which  all  tables  of  this  kind  are  subject,  which 
begin  the  year  with  January,  in  calculating  the  times 
of  new  or  full  Moons. 

The  mean  anomalies  of  the  Sun  and  Moon,  and 
the  Sun's  mean  motion  from  the  ascending  node  of 
the  Moon's  orbit,  are  set  down  in  Table  III.  from 
one  to  13  mean  lunations. — These  numbers,  for  13 
lunations,  being  added  to  the  radical  anomalies  of  the 
Sun  and  Moon,  and  to  the  Sun's  mean  distance  from 
the  ascending  node,  at  the  time  of  mean  new  Moon 
in  March  1700,  (Table  I.)  will  give  their  mean  ano- 
malies, and  the  Sun's  mean  distance  from  the  node, 
at  the  time  of  mean  new  Moon  in  March  1701 ; 
and  being  added  for  12  lunations  to  those  for  1701, 
give  them  for  the  time  of  mean  new  Moon  in  March 
1702.  And  so  on,  as  far  as  you  please  to  continue 
the  table  (which  is  here  carried  on  to  the  year  1800), 
always  throwing  off  12  signs  when  their  sum  ex- 
ceeds 12,  and  setting  down  the  remainder  as  the 
proper  quantity. 

If  the  numbers  belonging  to  A.  D.  1700  (in  Ta- 
ble I.)  be  subtracted  from  those  belonging  to  1800, 
we  shall  have  their  whole  differences  in  100  com- 
plete Julian  years ;  which  accordingly  we  find  to  be 


The  Construction  of  the  following  Tables. 

4  days  8  hours  10  minutes  52  seconds  15  thirds  40 
fourths,  with  respect  to  the  time   of   mean  new 
Moon. — These  being  added  together  60  times,  (al- 
ways taking  care  to  throw  off  a  whole  lunation  when 
thQ  days  exceed  29|)  making  up  60  centuries,  or 
6000  years,  as  in  Table  VJ.  which  was  carried  on 
to  seconds,  thirds,  and  fourths;  and  then  written 
out  to  the  nearest  second.     In  the  same  manner 
were  the  respective  anomalies  and  the  Sun's  distance 
from  the  node  found,  for  these  centurial  years  ;  and 
then  (for  want  of  room)  written  out  only  to  the  near- 
est minute,  which  is  sufficient  in  whole  centuries. — 
By  means  of  these  two  tables,  we  may  find  the  time 
of  any  mean  new  Moon  in  Marchy  together  with 
the  anomalies  of  the  Sun  and  Moon,  and  the  Sun's 
distance  from  the  node,  at  these  times,  within  the 
limits  of  6000  years,  either  before  or  after  any  giv- 
en year  in  the  18th  century;  and  the  mean  time  of 
any  new  or  full  Moon  in   any  given  month   after 
March,  by  means  of  the  third  and  fourth  tables, 
within  the  same  limits,  as  shewn  in  the  precepts  for 
calculation. 

Thus  it  would  be  a  very  easy  matter  to  calculate 
the  time  of  any  new  or  full  Moon,  if  the  Sun  and 
Moon  moved  equably  in  all  parts  of  their  orbits. — 
But  we  have  already  shewn  that  their  places  are  ne- 
ver the  same  as  they  would  be  by  equable  motions, 
except  when  they  are  in  apogee  or  perigee  ;  which 
is  when  their  mean  anomalies  are  either  'nothing,  or 
six  signs  :  and  that  their  mean  places  are  always  for- 
warder than  their  true  places,  while  the  anomaly  is 
less  than  six  signs  ;  and  their  true  places  are  for- 
warder than  the  mean,  while  the  anomaly  is  more. 

Hence  it  is  evident,  that  while  the  Sun's  anomaly 
is  less  than  six  signs,  the  Moon  will  overtake  him, 
or  be  opposite  to  him,  sooner  than  she  could  if  his 
motion  were  equable  ;  and  later  while  his  anomaly 
is  more  than  six  signs.  The  greatest  difference  that 
can  possibly  happen  between  the  mean  and  true  time 


324  The  Construction  of  the  following  Tables. 

of  new  or  full  Moon,  on  "account  of  the  inequality 
of  the  Sun's  motion,  is  three  hours  48  minutes 
28  seconds  :  and  that  is,  when  the  Sun's  anomaly 
is  either  3  signs  1  degree,  or  8  signs  29  degrees ; 
sooner  in  the  first  case,  and  later  in  the  last. — In  all 
other  signs  and  degrees  of  anomaly,  the  difference 
is  gradually  less,  and  vanishes  when  the  anomaly  is 
either  nothing  or  six  signs. 

The  Sun  is  in  his  apogee  on  the  30th  of  June, 
and  in  his  perigee  on  the  30th  of  December ,  in  the 
present  age  ;  so  that  he  is  nearer  the  Earth  in  our 
winter  than  in  our  summer.  The  proportional  dif- 
ference of  distance,  deduced  from  the  difference  of 
the  Sun's  apparent  diameter  at  these  times,  is  as 
983  to  1017. 

The  Moon's  orbit  is  dilated  in  winter,  and  con- 
tracted in  summer ;  therefore  the  lunations  are  long- 
er in  winter  than  in  summer.  The  greatest  differ- 
ence is  found  to  be  22  minutes  29  seconds ;  the  lu- 
nations increasing  gradually  in  length  while  the  Sun 
is  moving  from  his  apogee  to  his  perigee,  and  de- 
creasing in  length  while  he  is  moving  from  his  pe- 
rigee to  his  apogee. — On  this  account  the  Moon 
will  be  later  every  time  in  coming  to  her  conjunc- 
tion with  the  Sun,  or  being  in  opposition  to  him, 
from  December  till  June^  and  sooner  from  June  to 
December,  than  if  her  orbit  had  continued  of  the 
same  size  all  the  year  round. 

As  both  these  differences  depend  on  the  Sun's 
anomaly,  they  may  be  fitly  put  together  into  one  ta- 
ble, and  called  The  annual,  or  first  equation  of  the 
mean  to  the  true*  syzygy  (see  Table  VII.)  This 
equational  difference  is  to  be  subtracted  from  the 
time  of  the  mean  syzygy  when  the  Sun's  anomaly 
is  less  than  six  signs,  and  added  when  the  anomaly 
is  more. — At  the  greatest,  it  is  4  hours  10  minutes 
57  seconds,  viz.  3  hours  48  minutes  28  seconds. 

*  The  word  syzygy  signifies  both  the  conjunction  and  opposition 
of  the  Sun  and  Moon/ 


The  Construction  of  the  following. Tables.  325 

i 

on  account  of  the  Sun's  unequal  motion,  and  22 
minutes  29  seconds,  on  account  of  the  dilatation  of 
the  Moon's  orbit. 

This  compound  equation  would  be  sufficient  for 
reducing  the  mean  time  of  new  or  full  Moon  to  the 
true  time,  if  the  Moon's  orbit  were  of  a  circular 
form,  and  her  motion  quite  equable  in  it. — But  the 
Moon's  orbit  is  more  elliptical  than  the  Sun's,  and 
her  motion  in  it  so  much  the  more  unequal.  The 
difference  is  so  great,  that  she  is  sometimes  in  con- 
junction with  the  Sun,  or  in  opposition  to  him,  soon- 
er by  9  hours  47  minutes  54  seconds,  than  she 
would  be  if  her  motion  were  equable ;  and  at  other 
times  as  much  later. — The  former  happens  when 
her  mean  anomaly  is  9  signs  4  degrees,  and  the  lat- 
ter when  it  is  2  signs  26  degrees.  See  Table  IX. 

At  different  distances  of  the  Sun  from  the  Moon's 
apogee,  the  figure  of  the  Moon's  orbit  becomes  dif- 
ferent.— It  is  longest  of  all,  or  most  eccentric,  when 
the  Sun  is  in  the  same  sign  and  degree  either  with 
the  Moon's  apogee  or  perigee  ;  shortest  of  all,  or 
least  eccentric,  when  the  Sun's  distance  from  the 
Moon's  apogee  is  either  three  signs  or  nine  signs  ; 
and  at  a  mean  state  when  the  distance  is  either  1  • 
sign  15  degrees,  4  signs  15  degrees,  7  signs  15  de- 
grees, or  10  signs  15  degrees. — When  the  Moon's 
orbit  is  at  its  greatest  eccentricity,  her  apogeal  dis- 
tance from  the  Earth's  centre  is  to  her  perigeal 
distance  from  it,  as  106  7  is  to  933  ;  when  least  ec- 
centric, as  1043  is  to  957;  and  when  at. the  mean 
state,  as  1055  is  to  945. 

But  the  Sun's  distance  from  the  Moon's  apogee 
is  equal  to  the  quantity  of  the  Moon's  mean  ano- 
maly at  the  time  of  new  Moon,  and  by  the  addition 
of  six  signs,  it  becomes  equal  in  quantity  to  the 
Moon's  mean  anomaly  at  the  time  of  full  Moon. — 
Therefore,  a  table  may  be  constructed  so  as  to  answer 
all  the  various  inequalities  depending  on  the  different  • 
eccentricities  of  the  Moon's  orbit  In  the  syzygies  ; 
and  called  The  second  equation  of  the  mean  to  the  true 


326  The  Construction  of  the  following  Tables. 

syzygy  (see  Table  IX.)  and  the  Moon's  anomaly, 
when  equated  by  Table  VIII.  may  be  made  the 
proper  argument  for  taking  out  this  second  equa- 
tion of  time,  which  must  be  added  to  the  former 
equated  time,  when  the  Moon's  anomaly  is  less  than 
six  signs,  and  subtracted  when  the  anomaly  is  more. 
There  are  several  other  inequalities  in  the  Moon's 
motion,  which  sometimes  bring  on  the  true  syzygy 
a  little  sooner,  and  at  other  times  keep  it  back  a 
little  later  than  it  would  otherwise  be ;  but  they  are 
so  small,  that  they  may  be  all  omitted  except  two ; 
the  former  of  which  (see  Table  X.)  depends  on  the 
difference  between  the  anomalies  of  the  Sun  and 
Moon  in  the  syzygies,  and  the  latter  (see  Table 
XL)  depends  on  the  Sun's  distance  from  the  Moon's 
nodes  at  these  times.  The  greatest  difference  aris- 
ing from  the  former,  is  4  minutes  58  seconds;  and 
from  the  latter,  1  minute  34  seconds. 

Having  described  the  phenomena  arising  from  the 
inequalities  of  the  solar  and  lunar  motions^  we 
shall  now  shew  the  reasons  of  these  inequalities. 

In  all  calculations  relating  to  the  Sun  and  Moon, 
we  consider  the  Sun  as  a  moving  body,  and  the 
Earth  as  a  body  at  rest  j  since  all  the  appearances 
are  the  same,  whether  it  be  the  Sun  or  the  Earth  that 
moves.  But  the  truth  is,  that  the  Sun  is  at  rest,  and  the 
Earth  moves  round  him  once  a  year,  in  the  plane 
of  the  ecliptic.  Therefore,  whatever  sign  and  de- 
gree of  the  ecliptic  the  Earth  is  in,  at  any  given 
time,  the  Sun  will  then  appear  to  be  in  the  oppo- 
site sign  and  degree. 

The  nearer  that  any  body  is  to  the  Sun,  the  more 
it  is  attracted  by  him;  and  this  attraction  increases 
as  the  square  of  the  distance  diminishes ;  and  vice 
versa. 

The  Earth's  annual  orbit  is  elliptical,  and  the  Sun 
is  placed  in  one  of  its  focuses.  The  remotest  point 


The  Construction  of  the  following  Tables.  327 

of  the  Earth's  orbit  from  the  Sun  is  called  The 
earth* s  aphelion;  and  the  nearest  point  of  the  Earth's 
orbit  to  the  Sun,  is  called  The  Earth's  perihelion. — 
When  the  Earth  is  in  its  aphelion,  the  Sun  appears 
to  be  in  its  apogee  ;  and  when  the  Earth  is  in  its  pe- 
rihelion,  the  Sun  appears  to  be  in  its  perigee. 

As  the  Earth  moves  from  its  aphelion  to  its  pe- 
rihelion, it  is  constantly  more  and  more  attracted 
by  the  Sun ;  and  this  attraction,  by  conspiring  in 
some  degree  with  the  Earth's  motion,  must  neces- 
sarily accelerate  it.  But  as  the  Earth  moves  from 
its  perihelion  to  its  aphelion,  it  is  continually  less 
and  less  attracted  by  the  Sun ;  and  as  this  attrac- 
tion acts  then  just  as  much  against  the  Earth's 
motion,  as  it  acted  for  it  in  the  other  half  of  the 
orbit,  it  retards  the  motion  in  the  like  degree.— 
The  faster  the  Earth  moves,  the  faster  will  the 
Sun  appear  to  move  ;  the  slower  the  Earth  moves, 
the  slower  is  the  Sun's  apparent  motion. 

The  Moon's  orbit  is  also  elliptical,  and  the  Earth 
keeps  constantly  in  one  of  its  focuses. — The  Earth's 
attraction  has  the  same  kind  of  influence  on  the 
Moon's  motion,  as  the  Sun's  attraction  has  on  the 
motion  of  the  Earth  :  and  therefore,  the  Moon's 
motion  must  be  continually  accelerated  while  she 
is  passing  from  her  apogee  to  her  perigee  ;  and  as 
gradually  retarded  in  moving  from  her  perigee  to 
her  apogee. 

At  the  time  of  new  Moon,  the  Moon  is  nearer 
the  Sun  than  the  Earth  is  at  that  time,  by  the  whole  * 
semidiameter  of  the  Moon's  orbit ;  which,  at  a 
mean  state,  is  240,000  miles ;  and  at  the  full,  she 
is  as  much  farther  from  the  Sun  than  the  Earth 
then  is. — Consequently,  the  Sun  attracts  the  Moon 
more  than  it  attracts  the  Earth  in  the  former  case, 
and  less  in  the  latter.  The  difference  is  greatest 
when  the  Earth  is  nearest  the  Sun,  and  least  when 
it  is  farthest  from  him.  The  obvious  result  of  this 
is,  that  as  the  Earth  is  nearest  to  the  Sun  in  winter, 

Tt 


The  Construction  of  the  following  Tables. 

and  farthest  from  him  in  summer,  the  Moon's  or.- 
bit  must  be  dilated  in  winter,  and  contracted  in 
summer. 

These  are  the  principal  causes  of  the  difference 
of  time,  that  generally  happens  between  the  mean 
and  true  times  of  conjunction  or  opposition  of  the 
Sun  and  Moon.  As  to  the  other  two  differences, 
'viz.  those  which  depend  on  the  difference  between 
the  anomalies  of  the  Sun  and  Moon,  and  upon  the 
Sun's  distance  from  the  lunar  nodes,  in  the  syzy- 
gies,  they  are  owing  to  the  different  degrees  of  at- 
traction of  the  Sun  and  Earth  upon  the  Moon,  at 
greater  or  less  distances,  according  to  their  respec- 
tive anomalies,  and  to  the  position  of  the  Moon's 
tiodes  with  respect  to  the  Sun. 

If  ever  it  should  happen,  that  the  anomalies  of 
both  the  Sun  and  Moon  were  either  nothing  or  six 
signs,  at  the  mean  time  of  new  or  full  Moon,  and 
the  Sun  should  then  be  in  conjunction  with  either 
of  the  Moon's  nodes,  all  ^he  above-mentioned 
equations  would  vanish,  and  the  mean  and  true 
time  of  the  syzygy  would  coincide.  But  if  ever 
-this  circumstance  did  happen,  we  cannot  expect; 
the  like  again  in  many  ages  afterward. 

Every  49th  lunation  (or  course  of  the  Moon 
from  change  to  change)  returns  very  nearly  to  the 
same  time  of  the  day  as  before.  For,  in  49  mean 
lunations  there  are  1446  days  23  hours  58  minutes 
29  seconds  25  thirds,  which  wants  but  1  minute 
SO  seconds  34  thirds  of  1477  days. 

In29530590851 08  days,thereare  lOOQOQOOOOOO 
mean  lunations  exactly  :  and  this  is  the  smallest 
number  of  natural  days  in  which  any  exact  num- 
ber of  mean  lunations  will  be  completed. 


Astronomical  Tables. 


129 


S  'TABLE  I.     The  mean  Time  of  JVew   Moon  in  March,   Old   Style,  S 
Ij       with  the  mean  Anomalies  of  the  Sun  and  Moon,  and  the  Sun'smean  ^ 
S       Distance  from  the  Moon's  Ascending  Node,  from  A.  D.  1700  to  S 
S       A.  D.  1800  incliifiiue.                                                                                  S 

Y.ofChr. 

Mean   New  Moon 
in  March. 

Sun's  mean 
Anomaly. 

Moon's  mean 
Anomaly. 

Sun'smeanDist.  ? 
from  the  Node.   ^ 

D.     H.     M.    S. 

SO7" 

s       0     '      " 

-    S 

S  1700 
\  1701 
S  1702 
<5  1703 
S  1704 

8      16      11      25 
27      13      44        5 
16     22     32     41 
6        7      21      18 
24        4      53      57 

8       19      58      48 
9        8      20      59 
8      27      36      51 
8      16      52      45 
9        5      14      54 

1    22   30  37 
0  28      7   42 
11      7   55   47 
9    17   43   52 
8  23   20  57 

6    14   31      7    S 
7  23    14      8    <J 
8      1    16   55    S 
8      9    19   42    ^ 

9    18      2   43    < 

S  1705 

%  if  oe 

S  1707 
vj  1708 

13      13      42      34 
2      22      31       11 
31      20        3      50 
10        4      52      27 

8      24      30      47 
8      13      46      39 
9        2        8      501 

8      21      24      43 

7392 
5    12   57      7 
4    18   34    13 
2   28   22    18 

9   26      5   30    S 
10      4      8    17    Jj 
11    12    51    18    S 
11    20   54      5    £ 

^  1709 
S  1710 
!j  1711 
S  1712 

29        2      25        7 
18      11      13     43 
7     20        2     20 
25      17      34      59 

9        9      46      54 
8      29        2      47 
8      18      18      39 
9        6      40      51 

2      3  59   24 
0    13   47   3C 
10  23   35    36 
9   29    12   42 

0   29    37      6    > 
1      7   39   54    S 
1    15   42   41    £ 
2    14  25   43    <» 

S  1713 
>  1714 
S  1715 
J.1716 

15        2      23      36 
4      11       12      13 
23        8      44      52 
11      17      33     29 

8      25      56      43 
8,15      12      35 
9        3      34      47 
8      22      50      39 

8      9      0   47 
6   ,18  48    5? 
5   24   25    57 
4     4    14      2 

3     2   28   30    £ 
3    10  31    17    S 
4    19    14    IS    S 
4  27    17     5    S 

«S  1717 
$1718 

S  1719 
Ij  1720 

1        2      22        5 
19      23      54      45 
9        8      43      22 
27        6      16        1 

8      12        6      32 
9        0      28      44 
3      19      44      37 
9        8        6      49 

2    14      2      8 
1    19   39    13 
11    29  27    18 

115      4  24 

5      5    19   52    S 
6    14      2   54    ^ 
6   22      5   41    S 
8      0  43   43    «J 

S  3722 
!j  1723 
S  1724 

16      15        4      38 
5      23      53      14 
24      21      25      54 
13        6      14     31 

8      27      22      4J 
8      16     38      33 
9        5        0      45 
8      24      16      37 

9    14   52   29 
7   24  40   34 
7      0    17   40 
5    10      5    45 

,8      8    51    29    £ 
8    16  54    16    S 
9    25    37    18    Jj 
10      3  40      5    S 

S  1725 
J  1726 
S  1727 
S  1728 

2      15        3        78      13      32      29 
21      12      35     47  9        1      54     41 
10      21      24      23^8      21       10      34 
,28      18      57        3J9        9      52      46 

3    19    53    50 
2   25   30   56 
1      5    19      1 
0    10   50      7 

10    11   42   52    S 
1      20   25    54    $ 
I      28   28   41    Ij 
7    11    42    S 

S  1729  13        3      45      40  8      28      48      39 
<J  1730    7      12      34      16j8<     18        4      31 
i  1731  26      10        6      56p        6      26      42 
^  1732  14      18     55     33J8      25      42      34 

10   20   44    12 
9      0   32    17 
8      6      9    23 
6    15   57   28 

15    14   29    S 
23    17    16    > 
3.   2     0    17    S 
3    10     3     4    ^ 

330 


Astronomical  Tables. 


s   ^ 

S 

s    • 

Moan  Ne\\ 

Moon 

Sun's  mean 

Moon's  mean 

Sun's  moan  Dh.      S 

s     S, 

in  Mai 

eh. 

Anoi 

naly. 

Anomaly. 

irom  tlic  Nodi;.      S 

S     ° 

? 

k.           ^"" 

s    ^ 

D. 

H. 

M 

s. 

S 

0 

' 

a 

s     0 

/       '/ 

s     U         '       "  S 

S  1733 

4 

3 

44 

9 

8 

14 

58 

26 

4    25 

45    33 

3    18      551S 

J;  1734 

23 

1 

16 

49 

J 

3 

20 

38 

4      1 

22    3f- 

4  26   48   53  j> 

S  1735 

12 

10 

3 

'2, 

8 

22 

36 

30 

2    11 

10   44 

5      4  5  1   40  S 

!j  1736 

0 

18 

54 

2 

8 

11 

52 

22 

0  20 

58   49 

5    12    54  27  S 

S  1737 

19 

16 

26 

42 

9 

0 

14 

34 

11    26 

35    55 

621    37   29  s 

S  1738 

9 

1 

15 

IB 

8 

19 

oO 

26 

10      6 

24      (• 

6   iJ'j    40    16  v, 

>  1739 

27 

22 

47 

5  cS 

9 

7 

52 

38 

9    12 

1      6 

3      8   23    18  S 

S  1740 

16 

7 

36 

31 

8 

27 

8 

30 

7   21 

49    11 

8    16  26      5  $ 

<>  1741 

5 

16 

25 

1  i 

8 

16 

24 

22 

6      1 

37    Ifc 

8   24  28   52  S 

S  1742 

« 

24 

13 

57 

52 

9 

4 

46 

34 

5      7 

14  22 

10      3    1  1    54  vj 

S  1743 

13 

22 

46 

27 

] 

24 

2 

27 

3    17 

2   27 

10      1    14   41  Ij 

S  1744 

2 

7 

35 

4 

3 

13 

18 

20 

1    26 

50   32 

10    19    17   2g  S 

S  1745 

21 

5 

7 

44 

9 

I 

40 

32 

1      2 

27   38 

11   28     0  80  t 

Jj  1746 

10 

13 

56 

20 

8 

20 

56 

24 

11    12 

15   4:- 

0     6     3    17  S 

3  1747 

29 

11 

29 

0 

9 

18 

36 

10    17 

52   49 

1    14  46    19  Jj 

%  1748 

17 

20 

17 

36 

3 

28 

34 

28 

8   27 

40  54 

1    22    49      5  £ 

S  1749 

7 

5 

6 

13 

8 

ir 

50 

20 

7     7 

28   59 

2      0   51    52  S 

S  1750 

26 

38 

5o 

9 

6 

12 

32 

6    13 

6      5 

3      9   34  53  Jj 

S  1751 

15 

11 

27  , 

29 

8 

2;> 

28 

24 

4  22 

54    1C 

3    17   37   40  S 

;?  1752 

3 

20 

16 

6 

8 

14 

44 

16 

3      2 

42    15 

3    35    40   27  Jj 

Ij  1753 

22 

17 

48 

45 

9 

3 

6 

28 

2      8 

19    2ll    5      4   23    28  Jj 

S  1754 

12 

2 

37 

2  2 

8 

22 

22 

20 

0    18 

7  2( 

5    12  26    15  S 

!£  1755 

1 

11 

35 

59 

8 

11 

38 

12 

10  27 

55   31 

5   20  29      2  !j 

S  1756 

19 

8 

58 

38 

9 

0 

0 

24 

10      3 

32   37 

6  29    12      3  S 

S  1757 

8 

17 

47 

15 

8 

19 

16 

16 

8    13 

20  42 

7      7    14  50  ^ 

5  1758 

27 

15 

19 

54 

9 

7 

38 

28 

7  28 

57  48 

8    15    57   52  £ 

'S  1759 

17 

0 

8 

31 

8 

26 

54 

20 

5   28 

45    54 

8   24     0   39  S 

i^  1760 

5 

8 

57 

8 

•j 

16 

10 

12 

4      8 

34      6 

9      2      3   26  S 

'S  1761 

24 

6 

29 

47 

9 

4 

<j2 

24 

3    14 

11      6 

10    10  46  27  S 

^  1762. 

13 

15 

18 

24 

8 

23 

48 

16 

1    23 

59    11 

10    18   49    14  {j 

V1763 

3 

0 

7 

1 

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13 

4 

8 

0     3 

47    16 

10  26   52      1  S 

£  1764 
S  1765 

20 
10 

21 
6 

39 

28 

4C 
17 

9 
8 

1 

20 

26 
42 

20 
13 

11      9 
9    19 

24  21 
12   26 

0      5   35      2  <| 

0    13   37  49  S 

5  1766 

29 

4 

0 

56 

g 

9 

4 

20 

8  24 

49    32 

1    22  20  51  s 

Astronomical  Tables. 


331 


ss 

T 

ABLE 

I,   concluded.      Old  Style.                               S 

Mean  New  Moon 

Sun's  mean 

Moon's  mean 

Sun's  menn  Dist.       S 

S     8, 

in  March. 

Anomaly. 

Anomaly. 

from  the  Node.           *> 

P 

ss 

*     ? 

57" 

H. 

M. 

i>. 

s 

0 

/ 

'/ 

S        0       '         " 

s      0 

/      n  ^ 

S  1767 

18 

12 

49 

33 

8 

28 

20 

17 

7      4    37   37 

2      0 

23   38  s 

^  1768 

6 

21 

38 

10 

3 

17 

36 

9 

5    14   25   42 

2      8 

26  25  > 

S  1769 

£5 

19 

10 

40 

9 

5 

58 

21 

4  20     2   48 

3    17 

9   27  > 

^  1770 

15 

3 

59 

26 

8 

25 

14 

13 

2   29   50   53 

3   25 

12    14S 

S  1771 

4 

12 

48 

2 

8 

14 

30 

5 

1      9   38    58 

4      3 

15      1  £ 

S  1772 

22 

10 

20 

43 

9 

2 

52 

17 

0    15    16      4 

5    11 

58      3  S 

!j  1773 

11 

19 

9 

19 

8 

22 

8 

9 

10  25      4      9 

5   20 

0   50  s 

S  1774 

1 

s 

57 

55 

8 

11 

24 

1 

9      4   52    14 

5   28 

3   37  £ 

S  1775 

20 

1 

30 

25 

8 

29 

46 

13 

8    10  29   20 

7     6 

49   38  s 

S  1776 

8 

10 

19 

12 

8 

19 

2 

5 

6   20    17   25 

7    14 

49   25  S 

S  1777 

27 

7 

51 

51 

y 

7 

24 

17 

5   25   54   31 

8   23 

32   26  S 

^  1778 

16 

16 

40 

28 

8 

26 

40 

9 

4      5   42   36 

9      1 

35    13  <j 

S  1779 

6 

1 

29 

4 

a 

15 

56 

1 

2    15    30  41 

9      9 

38     0  S 

!j  1780 

23 

23 

1 

44 

9 

4 

IB 

IS 

1   21      7  47 

10    18 

21      1  <J 

S  1781 

13 

7 

50 

21 

8 

23 

34 

5 

0     0   55   52 

10   26 

23   48  S 

^  1782 

2 

16 

38 

57 

8 

12 

49 

58 

10    10  43   57 

11      4 

26   35  S 

Jj  1783 

21 

14 

11 

37 

9 

1 

12 

10 

9    16£1      3 

0    1.3 

9   36  \ 

S  1784 

9 

23 

0 

13 

a 

20 

28 

3 

7  26     9     8 

0   21 

12   23  S 

£  1785 

28 

20 

32 

53 

9 

8 

50 

15 

7      1    46    14 

1    29 

55    25  Sj 

S  1786 

18 

5 

21 

30 

8 

28 

6 

7 

5    11    34    19 

2     7 

58    12  S 

S  1787 

7 

14 

10 

6 

8 

17 

21 

59 

3   21    22   24 

2    16 

0   59  *» 

S  1788 

25 

11 

42 

46 

9 

5 

44 

11 

2   26   59   30 

3   24 

44      1  5 

^  1789 

14 

20 

31 

23 

8 

25 

0 

3 

I      6  47   35 

4     2 

46  48  S 

S  1790 

4 

5 

19 

59 

8 

14 

15 

55 

11    16   35   40 

4    10 

49   35  ^ 

S  1791 

23 

2 

52 

39 

9 

2 

38 

7 

10  22    12   46 

5    19 

32   37  S 

%  1792 

11 

11 

41 

15 

8 

21 

53 

59 

9      2      0   52 

5   27 

35   24  S 

S  1793 

30 

9 

13 

55 

9 

10 

16 

11 

8      7   37  58 

7     6 

18   26  ^ 

S  1794 

19 

18 

2 

32 

8 

29 

32 

3 

6   17   26     4 

7    14 

21    13  S 

S  1795 

9 

2 

51 

8 

8 

18 

47 

55 

4  27    14     9 

7   22 

24     0  s 

S  179G 

27 

0 

23 

48 

9 

7 

10 

7 

4      2   51    14 

9      1 

7      1  S 

S  1797 

16 

9 

12 

24 

8 

26 

25 

59 

2    12   39    19 

9      9 

9   48  S 

I;  1798 

5 

18 

1 

1 

3 

15 

41 

51 

0  22   27   25 

9    17 

12    35  !{ 

S  1799 

24 

15 

23 

41 

J 

4 

4 

3 

11    28      4   31 

10  25 

-  -      n-f    L 

DJ   37  S 

I}  1800 

13 

0 

22 

178 

23 

19 

55  10     7   52   36 

11      3 

58   22  ^ 

33: 


Astronomical  Tables. 


J  TABLE 

II. 

Mean 

New 

Moon 

,   &c.  in   March,   New    Style,  from  :  S 

S 

A.  D 

.  1752 

to  A 

.  D.  1800. 

> 

S       0 

1 

Mean  New  Moon 

Sun's  mean 

Moon's  mean 

S 

Sun's  mean  Dist.      ? 

C           t-tl 

in  March. 

Anomaly. 

Anomaly. 

ii-om  the  Nodi-.          ^ 

s    o 

S 

s 

s     ? 

D. 

H 

M. 

s. 

s           0         '            " 

S         0       ' 

// 

s     0       '       ^Jj 

S   1752 

14 

20 

16 

6 

8 

14 

44 

16 

3      2    42 

15 

3    25   40   27  S 

S  1753 

4 

5 

4 

42 

8 

4 

0 

8 

1    12   30 

20 

4     3   43    14  ^ 

S  1754 

23 

2 

37 

22 

S 

22 

22 

20 

0    18     7 

26 

5    12   26    15  S 

V 

•S  1755 

12 

11 

25 

59 

8 

11 

38 

12 

10   27   55 

31 

5   20   29      2  Sj 

S  1756 

30 

8 

58 

38 

9 

0 

0 

24 

10      3   32 

37 

6   29    12      3  S 

S  1757 

19 

17 

47 

15 

8 

19 

16 

16 

8    13   20 

42 

7      7    14  50  S 

^  1758 

9 

2 

35 

51 

8 

8 

32 

8 

6   23      8 

47 

7    15    17   38  £ 

S  1759 

28 

0 

8 

31 

8 

26 

54 

20 

5    28   45 

54 

8   24     0   39  : 

^  1760 

16 

8 

57 

8 

8 

i5 

10 

12 

4      8   34 

0 

9      2      3  £6  s 

S  1761 

5 

17 

45 

44 

S 

5 

26 

4 

2    18   22 

5 

9    10      6    13  S 

S  1762 

24 

15 

18 

24 

8 

23 

48 

16 

1    23   59 

1  1 

10    18   49    14  S 

J>  1763 

14 

0 

7 

i 

8 

13 

4 

8 

0      3   47 

16 

10   26   52      1  ^ 

S  1764 

2 

8 

55 

36 

8 

2 

20 

0 

10    13   35 

21 

11      4   54  48  S 

>  1765 

21 

6 

28 

17 

8 

20 

42 

13 

9    19    12 

2G 

0    13   37  49  Jj 

S  1766 

10 

15 

16 

53 

a 

9 

58 

5 

7   29     0 

3  i 

0  21    40   37  S 

£  1767 

29 

12 

49 

33 

8 

28 

20 

17 

7     4  37 

J7 

2      0   23   38  S 

>  1768 

17 

21 

38 

9 

8 

17 

36 

9" 

5    14   25 

42 

2      8   26  25  lj 

S  1769 

7 

6 

26 

46 

8 

6 

52 

1 

3   24    13 

47 

2    16   29    13  S 

J  1770 

26 

3 

59 

86 

8 

25 

14 

1  3 

2   29   50 

53 

3   25    12    14  Jj 

S  1771 

15 

12 

48 

2 

8 

14 

so 

5 

1      9   38 

58 

4      315      IS 

S  177^ 

3 

21 

36 

39 

a 

3 

45 

57 

11    19   27 

S 

411    17   48  S 

Jj  1773 

22 

19 

9 

19 

8 

22 

8 

Q 

10  25      4 

9 

5   20     0  50  £ 

S  17T4 

12 

3 

5? 

55 

8 

11 

24 

1 

9      4  52 

14 

5   28      3   37  S 

^  1775 

1 

12 

46 

3  1 

8 

0 

39 

53 

7    14  40 

19 

6      6      6   24  > 

S  1776 

19 

10 

19 

12 

8 

19 

2 

5 

6   20    17 

25 

7    14  49   25  S 
( 

S  1777 

8 

19 

7 

48 

8 

8 

17 

57 

5      Q      5 

30 

7   22    52    12  s 

Jj  1778 

27 

16 

40 

28 

8 

26 

40 

9 

4      5   42 

.36 

9      1    35    13  S 

S  1779 

17 

1 

29 

4 

8 

15 

56 

1 

2    15    30 

41 

9     9   38     0  J 

^  1780 

5 

10 

17 

40 

3 

5 

11 

53 

0   25    18 

46 

9    17  40  47  S 

S  1781 

24 

7 

50 

21 

8 

23 

34 

5 

0      0   55 

52 

10  26  23   48  J 
—  t 

5  1782 

13 

16 

38' 

57 

8 

12 

49 

58 

10    10  43 

57 

il      4  26   35  ^ 

S  1783 

3 

1 

27 

33 

g 

2 

5 

50 

8   20   32 

2 

11    12   29   22  S 

S  1784 

20 

23 

0 

33 

8 

20 

28 

3 

9   26      9 

8 

0  21    12   23  £ 

S  1785 

10 

7 

48 

50 

8 

9 

43 

55 

6      5   57 

13 

0  29    15  .10  S 

S  1786 

29 

5 

21 

30 

8 

28 

6 

7 

5    11    34 

19 

2      7   58    12  Ij 

Astronomical  Tables. 


333 


S  '                      TABLE  II,    concluded.     New  Style.                      \ 

S     ^ 

^ 

v  1787 
S  1788 
S  1789 
>  1790 
S  1791 

Mean  New  Moon 
in  March. 

Sun's  mean 
Anomaly. 

Moon's  mean 
Anomaly. 

•> 

Sun's  mean  Dis.  /* 
from  the  Xode.    ? 

D.     H.    M.     S. 

s       0       '         " 

s     0      '       " 

sO'     "  S 

18     14     10       6 
6    22    58    42 
25     20    31    23 
15       5     19    59 
4     14      8     35 

8     17    21     59 
8       6    37    51 
8    25       0      3 
8     14     15     55 
8       3     31     47 

3  21  22  24 
2     1  10  29 
1     6  47  35 
11  16  35  40 
9  26  23  45 

2  16     9  59  c 
2  24    3  46  S 
4     2  46  48  S 
4  10  49  35  J 
4  18  52  22  5 

J  1792 
J  1793 
S  1794 
S  1795 
!j  1796 
S  1797 
J  1798 
J  1799 
S  180C 

22     11     41     15 
11     20    29    51 
30     18       2    32 
20      2    51      8 
8     11     39    44 

8     21     53     59 
8     11       9    51 
8     29    32      3 
8     18     47    55 
8      8       3    47 

9     2     0  52 
7  11  48  57 
6  17  26    4 
4  27  14    9 
3    7    2  14 

5  27  35  24  £ 
6     5  31  11  > 
7  14  21  13  S 

7  22  24    OS 
8    0  26  47  S 
y    9  ~9~48  S 
9  17  12  35  S 
9  25  15  22  J 
11     3  58  25  L 

27      9     12    2i 
16     18       1       1 

6      2    49    57 
25       0    22    17 

8     26     25     o9 
8     15     41     51 
8       4    57    4o 
8     23     19    55 

2  12  39  19 
0  22  27  25 
11     2  15  30 
10    7  52  36 

*.' 


ABLE  III.  Mean  Anomalies,  and  Sun's  mean  Distance  S 
from  the  Node,  for  1  3-|  mean  Lunations.  <J 


No. 

Mean 
Lunations. 

Sun's  mean 
Anomaly. 

Moon's  mean 
Anomaly. 

Sun's  mean  Dis.  S 
from  the  Node.     £> 

D.   H.    M.     S- 

S         0        '         " 

s    0     '     " 

S        0    '       "  S 

5 

29  12    44       3 
59     1    28       6 
88  14    12      9 
118     2    56     12 
147  15    40     15 

0    29      6     19 
1     28     12    39 
2     27    18    58 
3     26    25     17 
4     25     31    37 

0  25  49  0 
1  21  38  1 
2  17  27  1 
3  13  16  2 
4952 

1     0  40  14  £ 
2     1  20  28  ^ 
3    2     0  42  S 
4    2  40  56  S 
5     3  21  10  £ 

6 
7 
8 
9 
10 

177     4     14     18 
206  17      8     21 
-'36    5    52     24 
265  18     36     27 
295     7     20     30 

5     24     37     56 
6     23    4^     15 
7     22    50     35 
8     21     56    54 
9     21       3     14 

5     4  54  3 
6     0  43  3 
6  26  32  3 
7  22  21  4 
8  18  10  4 

6    4     1  24  S 
7    4  41  33  S 
8    5  21  52  > 
9    6     2    6  £ 
10    6  42  20  ? 

11 

13 

324  20      4    33 
354    8     48     30 
383  21     32    40 

10    20      9     33 
11     19     15     52 
0    18    22    12 

9  13  59  5 
10    9  48  5 
11     5  37  6 

11     7  22  34  £ 
0    82    47  s 
1     8  43     IS 

| 

14  18     22       2 

0     14     33     10 

6  12  54  30 

0  15  20    7  t 

334 


Astronomical  Tables, 


STABLE  IV.     The  Days  of  the  Year,  reckoned  from\ 

the  Beginning  of  March. 


r; 

1 

> 

I 

r; 

^ 

g 

rt 

ft 

0 

0 

f 

n 

O 

0 

r& 

f 

a  S 

S- 

1 

r1 

3 

n> 

^ 

03 
en 

r-t- 

3 

cr 

o 
cr 

cr 

5 

cr 

2 

1 

11 

- 

1 

••*•• 

32 

52 

93 

23 

154 

185 

215 

246 

s 

338  <J 

276 

307 

s  * 

2 

33 

53 

94 

24 

155 

186 

216 

247 

277 

308 

339  •* 

s  3 

3 

34 

54 

95 

25 

156 

187 

217 

248 

278 

309 

340  S 

S  4 

4 

35 

55 

96 

26 

157 

188 

218 

249 

279310 

341  % 

S  5 

s,  

5 

36 

56 

97 

27 

158 

189 

219 

250 

280311 

342  S 

S  6 

6 

37 

67 

98 

28 

159 

190 

220 

251 

281312 

343  Jj 

ss  r 

7 

38 

68 

99 

29 

160 

191 

221 

252 

282:313 

344  S 

S  8 

8 

39 

69 

100 

30 

161 

192 

222 

253 

283 

314 

345  it 

S  9 

9 

40 

70 

101 

31 

162 

193 

223 

254 

284 

315 

346  !j 

SlO 

10 

41 

71 

102 

32 

163 

194 

224 

255 

285 

316 

347  S 

L« 

11 

42 

72 

103 

133 

164 

195 

225 

256 

286 

317 

348  S 

*>  12 

[2 

43 

73 

104 

134 

165 

196 

226 

257 

287318 

349  S 

S  13 

13 

44 

74  105 

135 

166 

197 

227 

258 

288319 

350  \ 

S  ^4 

14 

45 

75 

106 

136 

167 

198 

228 

259 

289320 

351  S 

|l5 

15 

46 

76J107 

137 

168 

199 

229 

260 

290321 

352  % 

5  16 

16 

47 

77!10S 

138 

169 

200 

230 

261 

291 

322 

^3$ 

S.17 

17 

48 

78  109 

139 

170 

201 

231 

262 

292 

323 

354  J; 

S  13 

18 

49 

79 

110 

140 

171 

202 

232 

263 

293 

324 

355  S 

S  19 

19 

50 

80  111 

141 

172 

203 

233 

264 

294 

325 

356  £ 

^20 

20 

51 

81  112 

142 

173 

204 

234 

265 

295 

326 

357  ^ 

r 

\3i 

"•• 

21 

52 

82  11 

143  174 

205 

235 

266 

296 

327 

T 

358  £ 

S;*a 

22 

53 

83 

114 

144 

175 

206 

236 

267  297 

328 

359  S 

7 

23 

54 

8-1 

11 

145 

176 

207 

237 

268 

298 

329 

360s 

S24 

2455 

8^ 

lie 

146 

177 

208 

238 

269 

299 

330 

361  <J 

2556 

8€ 

>  11 

147 

m 

209 

239 

270 

300 

331 

362  S 

S 

2C 

.57 

87:118 

148 

m 

>21C 

240 

271 

301  332 

363  ^ 

S27 

'27 

'  5£ 

88  119 

14? 

>  18C 

)211 

241 

272 

302 

333 

364  S 

S2£ 

$26 

>  5£ 

1  89  12C 

15C 

)  181 

212 

242 

273 

303 

334 

365  s 

S  <!><: 

(2< 

)6C 

)  90  121 

151 

IBS 

5213 

243 

274 

304 

335 

366  £ 

|SC 

)3( 

)61 

911122 

15$ 

i8i 

J214 

244 

275 

305 

336 

^ 

t 

31 

L 

95 

> 

15^ 

18-1 

245 

1306 

i 

ss 

S_                       '                 -<^ 

Astronomical  Tables. 


TABLE  V.  Mean  Lunations  from  1  to  100000. 


Lunat. 

Days.  Decimal  Parts. 

Days. 

Hou. 

M. 

S. 

Th. 

£| 

1 

29.520590851080 

=  29 

12 

44 

3 

2 

2 

59.061181702160 

59 

1 

28 

6 

5 

57  S' 

3 

88.591772553240 

88 

14 

12 

9 

8 

55$   , 

4 

118.122363404320 

118 

2 

56 

12 

11 

53  S 

5 

147.652954255401 

147 

15 

40 

15 

14 

52.5! 

6 

177.183545106481 

177 

4 

24 

18 

17 

50  S 

7 

206.714135957561 

206 

17 

8 

21 

20 

48? 

8 

236.244726808641 

236 

5 

52 

24 

23 

47  S; 

9 

265.77531765972; 

265 

18 

36 

27 

26 

4S] 

10 

295.30590851080 

295 

7 

20 

30 

29 

43  S 

20 

590.61181702160 

590 

14 

41 

0 

59 

•el 

30 

885.91772553240 

885 

22 

1 

31 

29 

10  S  • 

40 

1181.22363404320 

1181 

5 

22 

1 

58 

53  v 

50 

-1476.52954255401 

1476 

12 

42 

32 

28 

36  S  : 

60 

1771.83545106481 

1771 

20 

3 

2 

58 

19? 

70 

2067.14135957561 

2067 

3 

23 

33 

28 

2  S 

80 

2362.44726808641 

2362 

10 

44 

3 

57 

46  S 

90 

2657.75317659722 

2657 

18 

4 

34 

27 

29  S 

100 

2953.0590851080 

2953 

1 

25 

4 

57 

12  J 

200 

5906.1181702160 

5906 

2 

50 

9 

54 

24  S 

300 

8859.1772553240 

8859 

4 

15 

14 

51 

36  §• 

400 

11812.2363404320 

11812 

5 

40 

19 

48 

48  > 

500 

14765.2954255401 

14765 

7 

5 

24 

46 

OS 

600 

17718.3545106481 

17718 

8 

30 

29 

43 

12  ** 

700 

20671.4135957561 

20671 

9 

55 

34 

40 

24  S1 

800 

23624.4726808641 

23624 

11 

20 

39 

3,7 

36  !*  : 

900 

26577.5317659722 

26577 

12 

45 

44 

34 

48  S. 

1000 

29530.590851080 

29530 

14 

10 

49 

32 

o  i 

2000 

59061.  18ir02160 

59061 

4 

21 

39 

4 

OS 

3000 

88591.772553140 

88591 

18 

32 

28 

36 

0  t 

4000 

118122,363404320 

118122 

8 

43 

18 

8 

OS 

5000 

147652.954255401 

147652 

22 

54 

7 

40 

0 

6000 

177183.545106481 

177183 

13 

4 

57 

12 

OS 

7000 

206714.135957561 

206714 

3 

15 

46 

44 

0  t 

8000 

236244.726801641 

236244 

17 

26 

36 

16 

0?i 

9000 

265775.317659722 

265775 

7 

37 

25 

48 

0  v  i 

10000 

295305.90851080 

295305 

21 

48 

15 

20 

os; 

20000 

590611.81702160 

590611 

19 

36 

30 

40 

of 

30000 

885917.72553240 

855917 

17 

24 

46 

0 

0 

40000 

1188223.63404320 

1188223 

15 

13 

1 

20 

l\ 

50000 

1476529.54255401 

1476529 

13 

1 

16 

40 

60000 

1771835.45106481 

1771835 

10 

49 

32 

0 

0  u 

70000 

2067141.35957561 

2067141 

8 

37 

47 

20 

OS 

80000 

2362447.26808641 

2362447 

6 

25 

2 

40 

i\ 

90000 

2657-753.17659722 

2657753 

4 

14 

18 

0 

100000 

2953959.0851080 

2953959 

3 

2 

33 

20 

°s 

336 


Astronomical  Tables. 


~C*.     ^^*  ^  •*  ^^^^^V^(^«^^»y\A<^,X'»Av^'^'*y\^s^»^.^>^/',A^Vys,^./',X'<y",>\A,y\/^^/>  r 

Jj  TABLE  VI.    The  first  mean  New  Moon,  with  the  mean  Anomalies  ' 
S       of  the  Sun  and  Moon$  and  the  Sun's  mean  Distance  from  the  As-  \ 
Jj    pending  Node,  next  after  complete  Centuries  of  Julian  Years. 

S  Luna- 
^  tions. 

•-<  '   ( 

re    C 
80   fr: 

First 

New  Moon 

-Min's  mean 
Anomaly 

Moon's  mean 
Anomaly 

Sun  from     < 
Node.        < 

D.  H.  M.  S. 

s       0       ' 

s       0 

so'; 

S     1237 
S    2474 
!;    3711 
S    4948 

100 
200 
300 
400 

4      8   1O  52 
8   16  21   44 
13     0  32   37 
17     8  43  29 

0        3      21 
0        6     42 
0     10        3 
0     13      24 

8      15      22 
5        0     44 
1      16        6 
10        1      28 

4  19    27  , 
9     8    55 
1   28    22 
6   17    49 

S    6185 
S    7422 
^     8658 
S     9895 

500 
600 
700 
800 

21    16  54  21 
26     1      5   14 
0  20  32     3 
5     4  42  55 

0     16     46 
0     20        7 
11      24     22 
11      27     34 

6     16     50 
3        2     12 
10     21      45 

777 

11  7  16 
3  26  44 
7  15  31 
0  4  58 

£  11132 
S  12369 
Jj  13606 
S  14843 

900 
1000 
1100 
1200 

9   12   53  47 
13  21      4  40 
18      5   15   32 

22   13   26  24 

014 
O       4     25 
0        7     46 
0117 

3     22     29 
0       7     51 
8     23      13 
5        8      35 

4  24  25 
9  13  53 
2  3  20 
6  22  47 

S  16080 
S  17316 
Ij  18553 
S  19790 

1300 
140O 
1500 
160O 

26  21   37   16 
1    17     4     6 
6      1    14  58 
10     9  25  50 

0     14     28 
11      18     43 
11      22        4 
11      25     25 

1      23      57 
9      13      30 
5     28     52 
2      14     14 

11  12  15 
312 
7  20  29 
0  9  56 

>  21027 
S  22264 
!j  23501 
S  24738 

170O 
1800 
1900 
2000 

14  17  36  42 
19      1   47  35 
23     9  58  27 
27   18     9   19 

11      28     46 
028 
O        5     29 
O        8      50 

10     29     36 
7     14     58 
4       O     20 
0     15     42 

4  29  23 
9  18  51 
2  8  18 
6  27  45 

S  25974 
Ij27211 
^  28448 
S  29685 

2100 
2200 
2300 
2400 

2   13   36     8 
6  21  47     1 
11      5  57  53 

15   14     8  45 

11      13        5 
11      16     26 

11      19     47 
11      23        8 

8        5      15 

4     20     37 
1        5     59 
9     21      21 

10  16  32 
360 
7  25  27 
0  14  54 

S  30922 
\  32159 
S  33396 
S  34632 

2500 
2600 
2700 
2800 

19  22   19  38 
24     6  30  30 
28   14  41   22 
3   10     8    11 

11      26     29 
11      29     50 
0        3      11 
11        7     76 

6        6     43 
2     22       4 
11        7     26 

6     26     59 

5  4  22 
9  23  49 
2  13  16 
623 

S  35869 
§  37106 
S  38343 
S  39580 

2900 
3000 
3100 
3200 

7   18   19     3 
12     2  29  56 
16   10  40  48 
20  18  51  40 

11      1O     47 
11      14        8 
11      17     30 
11     20     51 

3      12     21 
11      27     43 
8      13        5 
4     28      27 

10  21  30 
3  10  58 
8  0  25 
0  19  52 

Astronomical  Tables. 


337 


s 

J                                     TABLE  VI.  concluded. 

>                                                                                     s 

S  Luna- 
^   tions. 
S  

^  40S  17 
S  42054 
I}  43290 
S  44527 

l*i  c~> 

rs  c^ 

P  1' 

IMl'St 

New  Moon. 

Sun's  mean 
Anomaly. 

.Moon's  mean 
Anomaly. 

bun's  mean    ? 
Dis.fromNode  ^ 

D.  H.    M.  S. 

s       0       ' 

s       0        ' 

s       0        '      \ 

3300 
3400 
3500 
3600 

25      3      2   33 
29    11    13  25 
4      6  40    14 
8    14   51      6 

\(      24      12 
11      27      33 
1           1      48 
1           5         9 

1       13      49 
9      29      11 
5      18      44 

2        4        6 

5         9      20  > 
9      28      47  S 
1       17      34> 
67         I? 

S  45701 
J  47001 
S  48238 
S  49475 

3700 
3800 
3900 
4000 

12  23      1    59 
17      7    12  51 
21    15   23  43 
25    23  34  35 

1           8      3(. 
1         11      51 
1         J5       12 

1         18      33 

10      19      28 
7        4      50 
3      20      12 
0        5      34 

10      26      29  s 
3      15,     56  S 
8        5'     23? 
0      24      50  J 

Ij  50711 
S  51948 
S  53185 
S  54422 
S  5*5659 
I*  56896 
5  58133 
\  59369 

4100 
4200 
4300 
4400 

0    19      1    27 
5      3    12    17 
6    11   23      9 
13    19   34      1 

10      22      48 
10      26        9 
10     29      31 
11        2      52 

7      25        7 
4      10      29 
0      25      51 
9      11       13 

4      13      37  S 

9        3        5<J 

1      22      32  £ 
6      \\      59  ^ 

4oOO 
4600 
4700 
4800 

13      3   44   54 
22    11   55  46 
26  20      6   38 
1     15   33  27 

11         6       13 
11        9      34 
11      12      55 
[0      17        « 

5      26      35 
2      1  1      57 

10     27      19 
6      16      52 

11         1      27s 
3      20      54  S 
8      10     21  ^ 
11      29        8S 

^  606^)6 
S  61843 
£  63080 
S  64317 

4900 
5000 
5100 
:>200 

5    23   44   20 
10      7  55    12 
\4    16      6      4 
19      0    16   56 

10      20      31 
.10      23      52 
10      27      13 
\\        0      34 

3        2      U 
11      17     30 

8        2      5H 
4      18      20 

4      18      36  S 
9        8         3  Ij 
1      27      30  S 
6      16      57? 

J?  66791 
?  68028 
!j  69265 

5  400 
5oOO 

23      8   27   4P 
27    16   38   41 
2    12      5   30 
6    20    16  22 

U        3      5a 
11        7      16 
10      11      31 
10      14      52 

1        3      42 
9      19        4 
5        8      37 
1      23      59 

H         6      25  ? 
2      25      52  S 
7      14      39  J 
04         6  S 

?  rirso 

!j  72976 

S  74212 

5700 

5803 
5900 
6000 

11      4  27    15 
15    12  38      7 
19   20  48   59 
24     4  59   52 

10      18       U 
10      21      35 
10      24      56 
10      28      17, 

i  0        9      2  i 
6      24      43 
3      10        5 
11      25      27 

4      23      34  S 
913        1  £ 
2        2      28  S 
6      21      56  S 

V 


If  Dr.  Pound's  mean  Lunation  (which  we  have  kept  by  in 
J>  making  these  tables)  be  added  74212  times  to  itself,  the  sum 
^  will  amount  to  6000  Julian  years  24  days  4  hours  59  minutes 
S  5 1  seconds  40  thirds ;  agreeing  with  the  first  part  of  the  last  S 
!ine  of  this  table,  within  half  a  second. 


UNIVERSITY  1 


OF 


338 


Astronomical  Tables. 


TABLE  V 


II.      The  annual,  tr  first  Equation  of  the  mean  S 
to  the  true  Syzygij.  ^ 


Argument.    Sun's  mean  Anomaly. 


Jj                                               Subtract.                                               ^ 

5°i 

s  « 

0 
Sign. 

1 
Sign. 

2 
Signs. 

o 

Signs. 

4 
Signs. 

5 

Signs. 

?'  i* 

H.M.S. 

H.M.S. 

H.M.S. 

H.M.S. 

H.M.S. 

H.  M.  S. 

S   o 

0      0      0 

2      3    12 

3    35      0 

4    10   53 

3   39    30 

2      7    45 

30  i; 

\  * 

|i 

0      4    18 
0      8    35 
•)    12   51 
0    17      8 
0  21    24 

3      6   55 
3    10    36 
2    14    14 
3    17   52 
2   21    27 

3   37    10 
3   39    18 
3  41    23 
3  43   26 

3   45    25 

i    10  57 

4    10   55 
4    10   49 
4    10   39 
4    10  24 

3   37    19 
3   35      6 
3   32   50 
3   30   30 

3   28      5 

2      355 
2     0      1 
I    56      5 
I    52      6 
1   48      4 

29  £ 
28  S 

27  S 
26? 
25  S 

0  25   39 
0   28   55 
0   34    11 
0  38   26 

0  42   39 

2   25      9 
2   28   29 
2   31    57 
2   35   22 
2   38   44 

3   47    19 
3  49      7 
3   50   50 
3   52  29 
3   54     4 

4    10      4 
4     9   39 
4     9    10 
4      8   37 

4      7   59 

3   25    35 
3   23      C 
3   20   20 
3    17   35 
3    14  49 

I   41      1 
I    39   56 
1    35   49 
1    31   41 
1    27   31 

24  S 
23  S 

?,\ 

20^ 

1  12 

'S  15 

0  46   52 
0   51      4 
0  55    17 
0   59   27 
I      3   36 

2   42      3 
2   45    18 
2   48   30 
2   51    40 
2   54  48 

3   55    35 

3   57     2 
3   58   27 
3   59   49 
3      1     7 

4      7    16 
4      6   29 
•i      5   37 
4      4  41 

4      3   40 

3    11    59 
396 
3      6    10 
3     3    10 
307 

1    23    19 
1    19      5 
1    14   49 
I    10  33 
i      6    15 

19  S 
18  1 

17  £ 

w; 

S  18 

S  19 

S20 

S22 
523 
S  24 

I      7   45 
i    11    53 
1    16     0 
1    20      6 
1   24    10 

2   57   53 
3     0  54 
3      3   51 
3      6  45 
3      9    36 

4      2    18 

4      3  23 
4      4   22 
4      5    18 
4      6    10 

4      2   35 
4      1    26 
t     0    12 
3   58   52 
3   57   27 

2   57      0 
2   53  49 
2   50  36 
2   47    18 
2   43   57 

1       1    56 
0   57   36 
0   53    15 
0  48   52 

0   44   28 

\3\ 
12  S 

!os 

28    12 
32    12 
36    10 
40      6 
44      1 

3    12   24 
3    15      9 
3    17   51 
3   20   30 
3  23     5 

4      6    58 
4      7  41 
4      8   21 
4      8   57 
4     9   29 

3    55    J>9 
3   54  26 
3   52   49 
3   51      9 
3   49   26 

2  40  35 
2   37      6 
2   33   35 
2   30     2 
2   26  26 

0  40      2 
0  35    36 
0  31    10 
0  26  44 
0  22    17 

9? 

i 

6S 

526 
S27 
^28 
S  29 
!j  30 

47  54 
51    46 
55   37 
t    59   26 
2      3    12 

3   25   36 
3   28      3 
3   30   26 
3  32  45 
3   35      0 

4     9   55 
4    10    16 
4    10   33 
4    10   45 
4    10  53 

3   47   38 
3  45  44 
3  43  45 
3  41    40 
3   39   30 

2   22   47 
2    19      5 
2    15   20 
2    11    35 
2     7  45 

0    17   50 
0    13   23 
0      8   56 
0      4  29 
000 

4  s 

2  S 

*!? 

S  05 

11 
Si^ns. 

10 
Signs. 

9 

Signs. 

8 

Signs. 

7 
Signs. 

6 
Signs. 

£                                              Add                                              C 

Astronomical  Tables. 


339 


tA9                                                                                                                                                                                                                                                                                                     .IWi 

S         TABLE  VIIL     Equation  of  the  Moon's  mean  Anomaly.         S 

S                            Argument.     Sun's  mean  Anomaly.                           J» 

S                                                  Subtract                                                  S 

s  c 

S  rt> 

_ 

S    ° 

1 

Li 

h 

1 

0 
Sign. 

1 
Sign. 

2 
Signs. 

3 
Signs. 

4 
Signs. 

5 

Signs. 

< 

G  s 

rt    S 

'J'-i      () 

0     '     " 

0     '      " 

0     '      " 

0      '         " 

0      '        " 

0    '      " 

000 

0  46  45 

1   21   32 

1     35       1 

1      23        4 

0  48    It) 

SOS 

0      1    37 
0     3    IS 
0      4   52 
0      6  28 
086 

0  48    10 
0  49   34 
0  50   53 
0   52    19 
0   53  40 

I   22  21 
1   23    10 
I   23   57 
1    24  41 
1   25   24 

1      35        2 
I      35         1 
1      35        0 
1      34     57 
1      34     50 

I      22      14 
1      21      24 
1      20     32 
1      19      38 
I      18     42 

0  46   51 
0  45   23 
0  43  54 
0  42   24 
0  40  5B 

29  ;» 

28? 
27  S 
26? 

S 

23  J; 

22  S 
21? 
20  Jj 

0     9   42 
0    11   20 
0    12   56 
0    14  33 
0    16    10 

0  55      0 
0   56  21 
0   57  38 
0   58   56 
1      0    13 

1    26     6 
I    26   48 
1   27  28 
1    28      6 

I    28   43 

1      34     43 
1      34     33 
I      34     22 
1      34        9 
I      33      53 

1      17     45 
1      16      48 
1      15     47 
1       14     44 
I      13     41 

0  39   21 
0  37  49 
0   36    15 
0   34  40 
0  33     5 

S  13 

S  14 

0    17  47 
0    19  23 
0  20  59 
0  22   35 
0  24    10 

1      1    29 
I      2  43 
1      3  56 
1      5      8 
1      6    18 

1    29    17 
1    29   51 
1    30  22 
1   30  50 
1    31    19 

I      33      37 
I      33      20 
1      33        0 
1      32      38 
1      32      14 

1      12      37 
1      11      33 
1      10     26 
1        9      17 
1        8        S 

0  31    31 

0  29   54 
0  28    18 
0  26  40 
0  25      3 

1  Q    T 

!«i 
'•I 

S  16 
S17 

J;i8 

S  19 
Ij  20 

0  25   45 
0  27    19 
0  28   52 
0   30  25 
0   31    57 

I      7  27 
1      8   36 
I      9   42 
1    10  49 
1    11    54 

1    31    45 
I    32    12 
1    32   34 
1    32   57 
I   33    17 

I    33   36 
I   33   52 
1   34     6 
1    34    18 
1    34  30 

1      3  1      50 
I      31      23 
I      30     55 
1      30     25 

1      29      54 

1        6      58 
1        5      46 
I        4      32 
1        3      19 
1        2         1 

0  23  23 
0   21    45 
0   20      7 
0    18   28 
0    16  48 

\t\ 

i; 
% 

8"S 

7  S 

\\ 

3  S 
2  S 

1 

pi 

!•? 

0  33  29 
0   35      2 
0  36   32 
0   38      1 
0   39  29 

1    12   58 
1    14      1 
1    15      1 
1    16     0 
1    16  59 

I      29      20 
1      28      45 
1      28        9 
1      27      30 
1      26      50 

1        0      45 
0      59      26 
0      58        7 
0      56     45 
0     55      23 

0    15      8 
0    13   28 
0    1  1    48 
0    10      7 
0      8   20 

26 
S27 
^-28 
^  29 
S  30 

^   CT3 

?    • 

0  40   59 
0  42  26 
0  43   54 
0  45    19 
0  47  45 

1    17   57 
1    18   52 
1    19   47 
1    20   40 
1    21    32 

I    34  40 
I    34  48 
1   34   54 
1    34   58 
1    35      1 

1      26     27 
I      25        5 
I      24      39 
1      23      52 
I      23        4 

0     54        1 
0     52      57 
0      51       12 
0      49      45 
0     48      19 

0      6  44 

053 
0      3   21 
0      1    40 
000 

6 
Signs. 

11 
Signs. 

10 
Signs. 

9 
Signs. 

8 
Signs. 

7 
Signs. 

j\ 

s                                                 Add                                                 J 

340 


Astronomical  Tables. 


TABLE  IX.   The  second  Equation  of  the  mean  to  the  true  S 
Argument.     Moon's  equated  Anomuiy.  c 


If 

0 
Sign. 

1 
Sign. 

2 
Signs. 

3 
Signs. 

4 
Signs. 

5 
Signs. 

cS 

\  ' 

H.M.S 

H.M.S 

H.M.S 

H.M.S 

H.M.S 

H.M.S 

1 

\:° 

000 

5  12  48 

8  47  8 

9  46  44 

8  8  59 

4  34  33 

30  Ij 

I1- 
\l- 

0  10  58 
0  21  56 
0  32  54 
0  42  52 
0  54  50 

5  21  56 
5  30  57 
5  39  51 
5  48  37 
5  57  17 

8  51  45 
8  56  10 
9  0  25 
9  4  31 
9  8  25 

9  45   3 
9  45  12 
9  44  11 

9  42  59 
9  41  36 

8  3  12 
7  57  23 
7  51  33 
7  45  46 
7  39  46 

4  26   1 
4  17  25 
4   8  47 
407 
3   1  23 

28  S 

27  s 

23  S 

! 

*i° 

1   5  48 
1  16  46 
1  27  44 
I  38  40 
1  49  33 

6  5  51 

6  14  19 
6  22  41 
6  30  57 
6  39  4 

9  12  9 
9  15  43 
9  19  5 
9  22  14 
9  25  12 

9  40   S 
9  38  19 
9  36  24 
9  34  18 
9  32   1 

7  33  36 
7  27  22 
7  21  2 
7  14  30 

7  7  50 

3  42  32 

o   no   o  o 
O   OO   OO 

3  24  42 
3  15  44 
3   6  45 

III 

20  ^ 

s  12 

S  13 

2  0  23 
2  11  10 
2  21  54 
2  32  34 

2  43   9 

6  47  0 
6  54  46 
7  2  24 
7  9  52 
7  17  9 

9  27  58 
9  30  32 
9  32  58 
9  35  12 
9  37  14 

9  29  33 
9  26  54 
9  24  4 
9  21   3 
9  17  51 

7  1  2 
6  54  8 
6  47  9 
6  40  6 
6  32  56 

2  57  45 
2  48  39 
2  39  34 
2  30  28 
2  21  19 

ill 

\\7 

V8 

Sl9 
S  20 

2  53  38 
343 

3  14  24 
3  24  42 
3  34  58 

7  24  10 
7  31  18 
7  58  9 
7  44  51 
7  51  24 

9  39  8 
9  40  51 
9  42  21 
9  43  42 
9  44  53 

9  14  28 
9  10  54 
979 
9   3  13 
8  59   6 

6  25  40 
6  18  18 
6  10  49 
6  3  16 
5  55  38 

2  12   8 
2  2  53 
53  36 
44  16 
34  54 

:sj 

"\ 

10 

Ij  22 

S  23 
5  24 

3  45  11 
3  55  21 
i  5  26 
4  25  26 
4  25  20 

7  57  45 
8  3  56 
8  9  57 
8  15  46 
8  21  24 

9  45  52 
9  46  38 
9  47  13 
9  47  36 
9  47  49 

8  54  5C 
8  50  24 
8  45  48 
8  41   2 
8  36   6 

5  47  54 
5  40  4 
5  32  9 
5  24  9 
5  16  5 

25  31 
16  7 
6  41 
0  57  13 
0  47  44 

»; 
*l 

\ll 

S  30 

4  35   6 

4  44  42 
4  54  11 
5  3  33 
5  12  48 

8  26  53 
8  32  11 
8  37  19 
8  42  18 
8  47  8 

9  47  54 
9  47  46 
9  47  33 
9  47  14 
9  46  44 

8  31   0 
8  25  44 
8  20  18 
8  14  33 
8   8  59 

5  7  56 
4  59  42 
4  51  15 

4  43  2 
4  34  33 

0  38  13 
0  28  41 
0  19  8 
0  9  34 
000 

4  <! 
3  £ 
2  S 
1  ^ 
0  J 

11 
Signs. 

10 
Signs. 

9 

Signs. 

8 

Signs. 

7 
Signs. 

6 

Signs. 

jfj 

ubtract 


Astronomical  Tables. 


341 


*>  TABLE  X.     The  third  Equati- 
Jj  onofthe  mran  to  the  true  Syzygvt 

TABLE  XI.    The  fourth  Equati-\ 
on  of  the  mean  to  the  true  Syzygy.  S 

S      drgumtnt.    Sun's  Anomaly. 
S              Moon's  Anomaly. 

Argument.    Sun's  mean  Distance  ^ 
from  the  Node.                S 

if 

s  ? 

Signs. 

Signs. 

Signs. 

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6  Adi1 

1  Suo 

7  Add 

2  Suo 

8  Ado 

it 
crc 

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M.  S. 

M.  S. 

M.  S 

M.  S. 

M.  S. 

M.  S. 

S    0 

0     0 

2  22 

4     12 

30 

0 

0     0 

1  22 

1  22 

30        <| 

Ij 

0    5 
0  10 
0  15 

0  20 

0  25 

2  26 
2  30 
2  34 
2  38 

2  42 

4     15 
4     18 
4     21 

4     24 
4     27 

29 

28 
27 
26 

25 

1 

^ 

0    4 
0     7 
0  10 
0  13 
0  16 

1  23 
1  24 
1  25 

1  26 
1  27 

1  21 
1  20 
1  18 
1  16 
1  14 

29        S 
28        ? 
27        s 
26       £ 
25        I 

S    6 
S    7 

S    9 
SlO 

0  30 
0  35 
0  40 
0  45 
0  50 

2  46 
2  50 
2  54 
2  58 
3    2 

4    30 
4    32 
4    34 
4    36 
4     38 

24 
23 
22 
21 
20 

6 
7 
8 
g 

10 

11 

12 
13 
14 
15 

0  20 
0  23 
0  26 
0  29 
0  32 

1  28 
1  29 
1  30 
1  31 
1  32 

1  12 
1  10 
1     8 
1     6 

1         0 

24    !; 

23        S 
22        > 
21        J 
20        S 

1 

0  55 
1     0 
1     5 
1  1C 
1  15 

1  20 
1  25 
1  30 
1  35 
1  4C 

1  45 
1  49 
1  52 
1  56 
2     0 

3    6 

3  10 
3  14 

3  Id 
3  22 

4    40 
4     42 
4    44 
4    46 
4    48 

19 
18 
17 
16 
15 

0  35 
0  38 
0  41 
0  44 
0  47 

1  33 
1  33 
1  34 
1  34 

1  34 

1     0 
0  57 
0  54 
0  51 
0  49 

19        J 
18        \ 
17        ? 
16        S 
15         ^ 

14        s 
13        S 
12        s 
11        S 
10        J 

11 

S  19 

3  26 
3  30 
3  34 
3  38 

3  42 

3  45 
3  48 
3  51 

3  54 
3  57 

4    50 
4    51 

4    52 
4    53 
4     54 

14 
13 
12 
11 
10 

9 
8 
7 
6 
5 

16 
17 

18 
19 

20 

0  50 
0  52 
0  54 
0  57 
1     C 

1  34 
1  34 
1  34 
1  33 
1  33 

0  45 
0  41 
0  37 
0  34 
0  31 

S  22 
?  23 

S24 

4     55 
4    56 
4    57 
4    57 
4    57 

4     58 
4    58 
4     58 
4    58 
4    58 

21 

22 
23 
24 
25 

1     2 
1     5 
1    8 
1  10 

1  12 

1  32 
1  31 
1  30 

1  28 

0  28 
0  25 
0  22 
0  19 
0  16 

9        S 
8        S 

7        % 
5        \ 

$26 
S27 
S2& 
S29 
30 

2    4 
2    9 
2  13 
2  18 

2  2? 

Signs. 

4     0 
4     3 
4    6 
4    9 

4  12 

4 
3 
2 
1 
0 

26 

27 
28 

29 
SO 

1  14 
1  16 
1  18 

1  20 
122 

1  27 
1  26 
1  25 
1  24 
1  22 

0  13 
0  10 
0    6 
0    3 
0     0 

n 

0        s 

$s 

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1     's 

w 

5  SUD 
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4  Suo 
10  Adc 

3   Sub. 
9  Add 

Subtract. 

342 


Astronomical  Tables. 


TABLE  XII.       The  Sun's  mean  Longitude^    Motion^  and    S 
Anomaly  ;    Old  Style.  \ 


J   cr 
S   o 

Sun's  mean 

Sun's  mean 

o 

Sun's  mean 

Sun's  mean  Jj 

Longitude. 

Anomaly. 

!» 

Motion. 

Anomaly.    S 

S 

P      2     nj 

"2.  £ 

<  5*3 
S  era 

s       o      f        // 

S              0             / 

rt>   & 

so/// 

•                0             /       S 

^        1 

9      7   53    10 

6     28      48 

19 

11   29   24   16 

29        4  <J 

J    201 

9     9   23  50 

6     26      57 

20 

0094 

29      48  S 

S    301 

9    10     9    10 

6     26        1 

40 

0     0    18      8 

29      37  $ 

!;  401 

9    10   54   30 

6     25        5 

60 

0     0  27    12 

29     26  S 

S     501 

9    11    39   50 

6      24        9 

80 

0     0   36    16 

1        29      15  s 

5  1001 

9    15   26  30 

6      19     32 

100 

0     0  45   20 

1        29        4  S 

S  1101 

9    16   11    50 

6      18     36 

200 

0      1   20   40 

1        28        8s 

?  1201 

9    16  57    10 

6      17     40 

300 

0     2    16     0 

1        27      12  S 

S  1301 

9    17  42  30 

6      16     44 

400 

0     3      1    20 

1        26      16  ? 

Jj  1401 

9    18   27   50 

6      15     49 

500 

0     3  46  40 

1        25      21  S 

S  1501 

9    19    13    10 

6      14     53 

600 

0     4  32     0 

1        24     25  S 

J  1601 

9    19   58   30 

6      13      57 

700 

0      5    17  20 

11      23      295 

S  1701 

9   20  43   50 

6      13        1 

800 

0     6     2  40 

11      22     33  S 

Jj  1801 

9   21    29    10 

6      12        6 

900 

0      6  48      0 

11      21      37^ 

L 

1000 

0     7  33  20 

11      20      1  1  < 

2  o 

V§  H 

Sun's  mean 
Motion. 

Sun's  mean 
Anomaly. 

2000 
3000 
400O 

0    15      6  40 
0  22  4*0     0 
1     0   13   20 

11      11      22j| 
11        2        3  ^ 

10     22     44  \ 

lu 

S              0           /            // 

S              0               / 

*i  \J\J\s 

5000 

1      7  46  40 

11  f     or\        r\ 

10,     13      25  « 

i  r\           A           tz. 

?           J 

11   29  45   40 

11     29     45 

6000 

15    20      0 

1U          4          O  $ 

5         2 

11   29   31    20 

11      29      29 

j 

3 

11    29    17     0 

11      29      14 

^ 

Sun's  mean 

Sun's  mean  j 

S        4 

0     0      1   49 

11      29     58 

§ 

Motion. 

Anomaly.    { 

S         5 

1  1    9Q    A1?    9C 

11        9Q        A  9 

53* 

1 

1  1     Zy    Ht  f     £y 

1       Zy       4.4 

01 

s        »      1       // 

S                0              /       (, 

S         6 

11   29   33     9 

11      29      27 

s 

S        7 

11   29    18  49 

11      29      11 

Jan. 

0000 

0        0        0^ 

S        8 

0     0     3  38 

11      29        5 

Feb. 

1      0   33    18 

1        0     33  J 

S        9 

11    29  49    18 

11      29     40 

Mar 

1   28     9    1 

1      28        9V 

S       10 

11   29   34  58 

11      29     24 

Apr. 

2  28  42   30 

2      28     42  \ 

S       11 

11   29   20  38 

11      29        9 

May 

3   28    16  40 

3     28      17  v 

^       12 

00     5   26 

11      29      53 

June 

4  28   49   58 

4     28     50  ^ 

S       13 

11   29   51      7 

11      29      37 

July 

5   28   24 

5      28     24  j 

J>       14 

1.1    29   36  47 

1  1      29      22 

Aug 

6  29   57  2 

6     28     57  v 

S       15 

11   29  22  27 

11      29        7 

Sept 

7  29   30  44 

7     29     30  ^ 

S        16 

0     0     7    15 

11      29      5C 

Oct. 

8  2'9     4  54 

8     29       4  ! 

S       17 

11    29  52   55 

11      29      35 

Nov 

9   29   38    12 

9     29     37  S 

<5       18 

11    29   38   35 

11      29      2C 

Dec 

10  29    12  22 

10     29      11  ^ 

Astronomical  1  \iblzs. 


343 


"S                                   TABLE  XII.  concluded.                                 \ 

4.                                                                                                                                                                                                                                                       f 

S 

Sun's  mean 

Sun's  mean 

Sun's  mean 

Sun's  mean 

Sun's  mean    s 

s 

Motion  and 

Motion  and 

Dist.  from 

Motion  and 

Dist.  from     S 

sst 

,  Anomaly. 

Anomaly. 

Node. 

Anomaly. 

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0      2   28 

0        2      36J31 

i  162: 

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ss  s 

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S    4 

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3 

0      7  24 

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[1    21    19 

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S    5 

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4 

0951 

0      10      23 

34 

1    23   47 

1      28      18  S 

S     6 

0      5    54   50 

5 

0    12    19 

0      12      50 

35 

1    26    15 

1      30      54  S 

ss  ^ 

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0    14  47 

0      15      35 

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1    28   42 

1      33      29  £ 

S    8 

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0    17    15 

0      18      11 

37 

1    31    10 

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S     9 

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0    19  43 

0      20     47 

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1      3.8     40  £ 

S  10 

0     9   51    23 

9 

0  22    11 

0      23      23 

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I    36      6 

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S  *  J 

0    10   50   32 

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0  24   38 

0      25      58 

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1    38   34 

1      43      52  £ 

S  12 

0    11    49   40 

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0  27      6 

0     28      34 

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1    41      2 

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S  13 

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I    43  30 

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S  14 

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0  32     2 

0      33      45 

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S  15 

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0   34   36 

0      36      21 

44 

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S  16 

0    15   46    IS 

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I    50   53 

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S  ^ 

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S  20 

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S  21 

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351      56 

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3     59      43 

53 

2    10   36 

2      17     38s 

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0  24  38   28 

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0  59      8 

1        219 

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S  In  leap-years,  after  February,  add  one  day,  and  one  day's  motion.  S 

S                                                                                                              S 

Xx 


Astronomical  '1  \ibles. 


-*?f 


A 


T 


ABLE  XI  If.    Equation  of  the  Surf*  Centre,   or  the  Dif- 
ference between  hi  a  wean  and  true  Place. 


Sun's  mean  Anomaly. 


Subtract. 


S  | 

<5 

0 
Sign. 

1 
Sign. 

2 
Signs. 

3 

Signs. 

4 
Signs. 

5 

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OS 

CD   > 

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rf  S 

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0   '  " 

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0   0   0 

0  56  47 

1  39   6 

i  55  37 

1  41  12 

0  58  53 

S  1 

s 

S  3 

S  5 

1 

s  1 

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0   1  59 
0  3  57 
0   5  56 
0  7  54 

0   9  52 

0  58  30 
1   0  12 
1   1  53 
1   3  33 
1   5  12 

1  40  7 
1  41   6 
1  42   3 
1  42  59 

1  43  52 

I  55  39 
1  55  38 
1  55  36 
1  55  31 
1  55  24 

1  40  12 
1  39  10 
1  38   6 
1  37  0 
I  35  52 

0  57  7 
0  55  19 
0  53  30 
0  51  40 

0  49  49 

29  S 
28  ^ 
27  S 
26^ 
25  S 

24  S 
23  S 
22  S 
31  S 
20  ? 

0  1  1  50 
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0  15  46 
0  17  43 
0  19  40 

1   6  50 
1   8  27 
1  10  2 
1  11  36 
1  13   9 

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I  45  34 
I  46  22 
1  47   8 
I  47  53 

1  55  15 
1  55   3 

I  54  50 
I  54  35 
1  54  17 

1  34  43 
1  33  32 
1  32  19 
1  31   4 
1  29  47 

0  47  57 
0  46   5 
0  44  11 
0  42  16 
0  40  21 

" 
» 

S  15 

Ma 

$  19 

^  20 

0  21  37 
0  23  33 

0  25  29 
0  27  25 
0  29  20 

1  14  41 
1  16  11 

1  17  40 
1  19   8 
1  20  34 

1  48  35 
1  49  15 
1  49  54 
1  50  30 
1  51   5 

\  53  57 
1  53  36 
1  53  12 
I  52  46 
1  52  18 

I  28  29 
1  27  9 
1  25  48 
1  24  25 
1  23  0 

0  38  25 
0  36  28 
0  34  30 
0  32  32 
0  30  33 

'9  S* 
18  S 

17? 

0  31  15 

0  33   9 
0  35   2 
0  36  55 
0  38  47 

1  21  59 
1  23  22 
1  24  44 
1  26  5 
1  27  24 

1  51  37 
I  52  8 
1  52  36 
1  53   8 
1  53  27 

1  51  48 
I  51  15 
1  50  41 
1  50   3 
1  49  26 

1  21  34 
1  20   6 
1  18  36 
1  17   5 
1  15  33 

0  28  53 
0  26  33 
0  24  33 
0  22  32 
0  20  30 

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10  S 

S21 
S  22 

S  24 
S  2o 

0  40  31J 
0  42  30 
0  44  20 
0  46  9 

0  47  57 

1  28  41 
1  29  57 
1  31  11 
1  32  25 
1  33  35 

1  53  50 

I  54  10 
1  54  28- 
1  54  44 
1  54  58 

1  48  46 
1  48   3 
1  47  19 
I  46  32 
1  45  44 

I  13  59 

1  12  24 
1  10  47 
1   9   9 
1   7  29 

0  18  28 
0  16  26 
0  14  24 
0  12  21 
0  10  18 

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8  S 
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0  49  45 
0  51  32 
0  53  18 
0  55   3 
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1  34  45 
1  35  53 
1  36  59 
1  38  S 
1  39   6 

1  55  10 
1  55  20 
1  55  28 
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I  44  53 
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9 
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7 
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6 
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S                    Add.                   J 

Astronomical  1  ables. 


345 


>  TABLE  XIV.   The  Sun's 

TABLE  XV.    Equation  of  the  Sun's  S 

<J              Declination. 

mean  Distance  from  the  Node.           ^ 

£  Argument,     Sun's  true  Place 

Argument,     Sun's   mean  Anomaly.           £ 

Signs 

signs. 

Signs. 

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, 

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346 


Astronomical  Tables. 


STABLE    XVI. 

vj        The     Moon't, 
S        Latitude     in 

\ 

TABLE  XVII.     The  Moon's  horizontal  Pa-    S 
rallax,  with  the  Semidiawcters  and  true  Ho-    ^ 
rary  Motion  of  the  &un  and  Moon,  and  eve-    S 
ry  tiixth  Degree  of  their  mean  Anomalies,     \ 
the  Quantities  for  the  intermediate  Degrees     S 
()>'.inp  easily  /iro/iortioned  by  Sight.                     \ 

-•                           •                       ,_m             t 

S  Argument,  Moon's 
S  equated  Distance 
£  from  the  Node. 

§    CD  H 
"^    f— 

MoCJn's 
horizor.t. 
Parallax. 

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m 

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6 
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18 

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54   29 

54   31 
54   34 
54   40 
54   47 

54   56 
55      6 
55    17 
55   29 
55   42 

55    56 
56   12 
56  29 
56  48 
57      8 

15    50 
15    50 
15    50 
15    51 
15    51 

14  54 
14  56 
14  56 
14  57 
14  58 

30    10 
30    12 
30    15 
30    19 
30  26 

2  23 
2  23 
2  23 
2  23 
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1  27  53 
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31      9 

31  2.; 

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2  24 
2  24 
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15    58 
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16      1 
16      2 
16      4 

15  17 
15  22 
15  26 
15  30 
15  36 

15  41 
15  46 
15  52 
15  58 
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31    56 
32    17 
32   39 
33    11 

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2  26 
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24  S 

18  S 
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6 
12 
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24 

57   30 
571  52 
53    12 
58   31 
58   49 

16      6 
16      8 
16    10 
16    11 
16    13 

33   23 
33   47 
34    11 
34   34 
34   58 

2  28 
2  2& 
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2  30 
2  31 
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s 

S.     5     Signs 

S  North-  Descending. 

4        0 
6 
12 
18 

24 

59      6 
59   21 
59    35 
•59   48 
60     0 

16    14 
15    15 
16    17 
16    19 

16   20 

16  9 
16  14 
16  10 
16  24 
16  28 

35   22 
35    45 
36     0 
36  20 
36  40 

37     0 
37    10 
37    19 

37  28 
37   36 

S       1  1     Signs 

^     South  Ascending. 

^  This  Table  shews 
S  the  Moon's  Lati- 
S  tude   a    little   be- 
S  yond  the    utmost 
Jj  Limits    of  Eclip- 
^ses. 

S 

5        0 
6 
12 
18 
24 

60    11 
60  21 
60  30 
60  38 

60  45 

16   21 
16   21 
16   22 
16   22 
16   23 

16  31 

16  32 
16  37 
16  38 
16  39 

2  32 
2  33 
2  33 
2  33 
2  33 

r    oj 

24  S 
12  J» 

6        0 

60  45 

16  23 

16  39 

37  40 

2  33 

60^ 

Precepts  relative  to  the  preceding  Tables.  347 


To  calculate  the  true  Time  of  New  or  Full  Moon. 

PRECEPT  I.  If  the  required  time  be  within  the 
limits  of  the  18th  century,  write  out  the  mean  time 
of  new  Moon  in  March,  for  the  proposed  year, 
from  Table  I,  in  the  old  style,  or  from  Table  II, 
in  the  new ;  together  with  the  mean  anomalies 
of  the  Sun  and  Moon,  and  the  Sun's  mean  dis- 
tance from  the  Moon's  ascending  node. — If  you 
want  the  time  of  full  Moon  in  March,  add  the 
half  lunation  at  the  foot  of  Table  III,  with  its 
anomalies,  &c.  to  the  former  numbers,  if  the* 
new  Moon  fall  before  the  15th  of  March;  but 
if  it  fall  after,  subtract  the  half  lunation,  with 
the  anomalies,  &c.  belonging  to  it,  from  the  for- 
mer  numbers,  and  write  down  the  respective  sums 
or  remainders. 

II.  In  these  additions  or  subtractions,  observe, 
that  60  seconds  make  a  minute,  60  minutes  make  a 
degree,    30  degrees  make  a  sign,    and    12  signs 
make  a  circle.     When  you  exceed  12  signs  in  ad- 
dition, reject   12,  and  set  down   the  remainder. — 
When  the   number  of  signs  to  be  subtracted  is 
greater  than  the  number  you  subtract  from,  add  12 
signs  to  the  lesser  number,  and  then  you  will  have 
a  remainder  to  set  down. — In  the  tables,    signs 
are  marked  thus  s,  degrees  thus  °,  minutes  thus  ', 
and  seconds  thus  ". 

III.  When  the  required   new   or  full  Moon  is 
in  any  given  month  after  March,  write  out  as  many 
lunations,  with  their  anomalies,  and  the  Sun's  dis- 
tance from  the  node,  from  Table  III.  as  the  given 
month  is  after  March;  setting  them  in  order  below 
the  numbers  taken  out  for  March. 

IV.  Add  all  these  together,   and  they  will  give 
the  mean  time  of  the  required  new  or  full  Moon, 
with  the  mean  anomalies  and  Sun's  mean  distance 
from  the  ascending  node,  which  are  the^arguments 
for  finding  the  proper  equations. 


Precepts  relating  to  the  preceding  Tables. 

V.  With  the  number  of  days  added  together, 
enter  Table  IV,  under  the  given  month,  and  against 
that  number  you   have  the  day  of  mean  new  or 
full   Moon   in   the  left-hand    column,    which    set 
before  the  hours,  minutes,  and  seconds,  already 
found. 

But  (as  it  will  sometimes  happen)  if  the  said 
number  of  days  fall  short  of  any  in  the  column 
under  the  given  month,  add  one  lunation  and  its 
anomalies,  &c.  (from  Table  III,  to  the  foresaid 
sums,  and  then  you  will  have  a  new  sum  of  days 
wherewith  to  enter  Table  IV,  under  the  given 
month,  where  you  are  sure  to  find  it  the  second 
time  if  the  first  fall  short. 

VI.  With  the  signs  and  degrees  of  the  Sim's 
anomaly,  enter  Table  VII,  and  therewith  take  out 
the  annual  or  first  equation  for  reducing  the  mean 
syzygy  to  the  true ;  taking  care  to  make  propor- 
tions in  the  table  for  the  odd  minutes  and  seconds 
of  anomaly,  as  the  table  gives  the  equation  only  to 
whole  degrees. 

Observe  in  this  and  every  other  case  of  finding 
equations,  that  if  the  signs  be  at  the  head  of  the 
table,  their  degrees  are  at  the  left  hand,  and  are 
reckoned  downward ;  but  if  the  signs  be  at  the 
foot  of  the  table,  their  degrees  are  at  the  right 
hand,  and  are  counted  upward;  the  equation  being 
in  the  body  of  the  table,  under  cr  over  the  signs, 
in  a  collateral  line  with  the  degrees. — The  titles 
Add  or  Subtract  at  the  head  or  foot  of  the  tables 
where  the  signs  are  found,  shew  \\Uether  the 
equation  is  to  be  added  to  the  mean  time  of  new 
or  full  Moon,  or  to  be  subtracted  from  it.  In 
this  table,  the  equation  is  to  be  subtracted  if  the 
signs  of  the  Suns  anomaly  be  found  at  the  head  of 
the  table ;  but  it  is  to  be  added,  if  the  signs  be  at 
the  foot. 

VII.  With  the  signs  and  degrees  of  the  Sun's 
mean  anomaly,    enter  Table  VIII,  and  take  out 


Precepts  relating  t.o  the  preceding  Dalies.  34!' 

the  equation  of  the  M  on's  mean  anomaly ;  subtract 
this  equation  from  her  mean  anomaly,  if  the  signs 
of  the  Sun's  anomaly  be  at  the  head  of  the  table, 
but  add  it  if  they  be  at  the  foot ;  the  result  will  be 
the  Moon's  equated  anomaly,  with  which  enter 
Table  IX,  and  take  out  the  second  equation  for  re- 
ducing the  mean  to  the  true  time  of  new  or  full 
Moon ;  adding  this  equation,  if  the  signs  of  the 
Moon's  anomaly  be  at  the  head  of  the  table,  but 
subtracting  it  if  they  be  at  the  foot,  and  the  result 
will  give  you  the  mean  time  of  the  required  new  or 
full  Moon  twice  equated,  which  will  be  sufficiently 
near  for  common  almanacks. — But  when  you  want 
to  calculate  an  eclipse,  the  following  equations  must 
be  used :  thus, 

VIII,  Subtract   the  Moon's  equated   anomaly 
from  the  Sun's  mean  anomaly,  and  with  the  re- 
mainder in  signs  and  degrees,  enter  Table  X,  and 
take  out  the  third  equation,  applying  it  to  the  former 
equated  time,  as  the  titles  Addvr  Subtract  do  direct. 

IX.  With  the  Sun's  mean  Distance  from  the  as- 
cending node  enter  Table  XI,  and  take  out  the 
equation  answering  to  that  argument,  adding  it  to, 
or  subtracting  it  from,  the  former  equated  time,  as 
the  titles  direct,  and  the  result  will  give  the  time 
of  new  or  full  Moon,  agreeing  with  well-regulated 
clocks  or  watches,  very  near  the  truth.     But,  to 
make  it  agree  with  the  solar,  or  apparent  time,  ap- 
ply the  equation  of  natural  days,  found  in  the  table 
(from  page  193  to  page  205)  as  it  is  leap-year,  or 
the  first,  second,  or  third  after. 

The  method  of  calculating  the  time  of  any  new 
or  full  Moon  without  the  limits  of  the  18th  century, 
will  be  shewn  further  on.  And  a  few  examples, 
compared  with  the  precepts,  will  make  the  whole 
work  plain, 

A".  B.  The  tables  begin  the  day  at  noon,  and 
reckon  forward  from  thence  to  the  noon  following. 
— Thus,  March  the  31st,  at  22h.  30min.  25sec.  of 
tabular  time,  is  April  1st  (in  common  reckoning)  at 
5scc.  after  10  o'clock  in  the  morning. 


350 


Precepts  and  Examples* 

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II   \  i-f-M 


relative  to  the  preceding  Tables* 


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To  calculate  the  Time  of  New  and  Full  Moon  in  a 
given  Tear  and  Month  of  any  particular  Century^ 
between  the  Christian  Mr  a  and  the  l&tb  Century. 

PRECEPT!.  Find  a  year  of  the  same  number  in 
the  1 8th  century  with  that  of  the  year  in  the  century 
proposed,  and  take  out  the  mean  time  of  new  Moon 
in  March,  old  style,  for  that  year,  with  the  mean 
anomalies  and  Sun's  mean  distance  from  the  node  at 
that  time,  as  already  taught. 

II.  Take  as  many  complete  centuries  of  years  from 
Table  VI.  as,  when  subtracted  from  the  abovesaid 
year  in  the  t  Sthcentury,  will  answer  tothe  given  year; 
and  take  out  the  first  mean  new  Moon  and  its  anoma- 
lies, &cf  belonging  to  the  said  centuries,  and  set  them 

Yy 


352  Precepts  and  Examples 

below  those  taken  out  for  March  in  the  1 8th  century. 

III.  Subtract  the  numbers  belonging  to  these  cen- 
turies, from  those  of  the  18th  century,  and  the  re- 
mainders will  be  the  mean  time  and  anomalies,  &c. 
of  new  Moon  in  March,  in  the  given  year  of  the  cen- 
tury proposed. — Then,  work  in  all  respects  for  the 
true  time  of  new  or  full  Moon,  as  shewn  in  the  above 
precepts  and  examples. 

IV.  If  the  days  annexed  to  these  centuries  exceed 
the  numberof  days  from  the  beginning  of  March  taken 
out  in  the  18th  century,  addalunation  and  its  anoma- 
lies &c.;from  Table,  III  to  the  time  and  anomalies  of 
new  Moon,  in  March,  and  then  proceed  in  all  respects 
as  above. — This  circumstance  happens  in  example  V. 


relative  to  the  preceding  Tables. 

To  calculate  the  true  Time  of  New  or  Full  Moon  in  any  given 
Year  and  Month  before  the  C/iristian  ./Era. 

PRECEPT  I.  Find  a  year  in  the  18th  century, 
which  being  added  to  the  given  number  of  years  be- 
fore Christ,  diminished  by  one,  shall  make  a  num- 
ber of  complete  centuries. 

II.  Find  this  number  of  centuries  in  Table  VI, 
and  subtract  the  time  and  anomalies  belonging  to  it 
from  those  of  the  mean  new  Moon  in  March,  the 
above-found  year  of  the  i8th  century  ;  and  the  re- 
mainder will  denote  the  time  and  anomalies,  &c.  of 
the  mean  new  Moon  in  March,  the  given  year  before 
Christ.  Then,  for  the  true  time  of  that  new  Moon, 
in  any  month  of  that  year,  proceed  in  the  manner 
taught  above 


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354 


Precepts  and  Examples 


These  tables  are  calculated  for  the  meridian  of 
London  ;  but  they  will  serve  for  any  other  place,  by 
subtracting  four  minutes  from  the  tabular  time,  for 
every  degree  that  the  meridian  of  the  given  place  is 
westward  of  London,  or  adding  four  minutes  for 
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relative  to  the  preceding  Tables. 


S55 


Tc  calculate  the  true  Time  of  New  or  Full  Moon>  in 
any  given  Tear  and  Month  after  the  1 8th  Century. 

PRECEPT  I.  Find  a  year  of  the  same  number  in 
the  1 8th  century  with  that  of  the  year  proposed,  and 
take  out  the  mean  time  and  anomalies  &c.  of  new 
Moon  in  March^  old  style,  for  that  year,  in  Table  I. 

II.  Take  so  many  years  from  Table  VI,  as,  when 
added  to  the  above-mentioned  year  in  the  18th  cen- 
tury, will  answer  to  the  given  year  in  which  the  new 
or  full  Moon  is  required:  and  take  out  the  first  new 
Moon,with  its  anomalies,  for  these  completecenturies. 


356 


Precepts  and  Examples 


III.  Add  all  these  together,  and  then  work  in  all  respects 
as  shewn  above,  only  remember  to  subtract  a  lunation  and 
its  anomalies,  when  the  above-mentioned  addition  carries  the 
new  Moon  beyond  the  31st  of  March  ;  as  in  the  following 
example  : 


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In  keeping  by  the  old  style,  we  are  always  sure  to  be 
right,  by  adding  or  subtracting  whole  hundreds  of  years 
to  or  from  any  given  year  in  the  18th  century.  But  in 
the  new  style  we  may  be  very  apt  to  make  mistakes,  on 
account  of  the  leap-years  not  coming  in  regularly  every 
fourth  year:  And  therefore,  when  we  go  without  the 


relative  to  the  preceding  Tables. 

limits  of  the  1 8th  century,  we  had  best  keep  to  the 
old  style,  and  at  the  end  of  the  calculation  reduce 
the  time  to  the  new.  Thus,  in  the  22d  century, 
there  will  be  14  days  difference  between  the  styles; 
and  therefore,  the  true  time  of  new  Moon  in  this 
last  example  being  reduced  to  the  new  style,  will  be 
the  22d  of  July,  at  22  minutes  53  seconds  past  VI 
in  the  evening. 

To  calculate  the  true  Place  of  the  Sun  for  any  given 
Moment  of  Time. 

PRECEPT  I.  In  Table  XII,  find  the  next  lesser 
year  in  number  to  that  in  which  the  Sun's  place  is 
sought,  and  write  out  his  mean  longitude  and  ano- 
maly answering  thereto:  to  which  add  his  mean  mo- 
tion and  anomaly  for  the  complete  residue  of  years, 
months,  days,  hours,  minutes,  and  seconds,  down 
to  the  given  time,  and  this  will  be  the  Sun's  mean 
place  and  anomaly  at  that  time,  in  the  old  style; 
provided  the  saidtime  bein  any  year  after  the  Chris- 
tian ^ra.  See  the  first  following  example. 

II.  Enter  Table  XIII  with  the  Sun's  mean  ano- 
maly, and  making  proportions  for  the  odd  minutes 
and  seconds  thereof,  take  cut  the  equation  of  the 
Sun's  centre:  which,  being  applied  to  his  mean 
place,  as  the  title  Add  or  Subtract  directs,  will  give 
his  true  place  or  longitude  from  the  vernal  equinox 
at  the  time  for  which  it  was  required. 

III.  To  calculate  the  Sun's  place  for  any  time  in 
a  given  year  before  the  Christian  sera,  take  out  his 
mean  longitude  and  anomaly  for  the  first  year  there- 
of, and  from  these  numbers,  subtract  the  mean  mo- 
tions and  anomalies  for  the  complete  hundreds  or 
thousands  next  above  the  given  year;  and  to  the 
remainders  add  those  for  the  residue  of   years, 
months,  &c.  and  then  work  in  all  respects  as  above. 
See  the  second  example  following. 


358 


Examples  from  the  preceding  Tables. 


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36t>  Concerning  Eclipses  of  the  Sun  and  Moon. 

So  that  in  the  meridian  of  London,  the  Sun  was 
then  just  entering  the  sign  =&  Libra,  and  conse- 
quently was  upon  the  point  of  the  autumnal  equi- 
nox. 

If  to  the  above  time  of  the  autumnal  equinox  at 
London,  we  add  2  hours  2  5  minures  4  seconds  for 
the  longitude  of  Babylon,  we  shall  have  for  the 
time  of  the  same  equinox,  at  that  place,  OctoberZSd, 
at  19  hours  22  minutes  41  seconds;  which,  in 
the  common  way  of  reckoning,  is  October  24th,  at 
22  minutes  41  seconds  past  VII  in  the  morning.* 

And  it  appears  by  example  VI,  that  in  the  same 
year,  the  true  time  of  full  Moon  at  Babylon  was 
October  23d,  at  42  minutes  46  seconds  after  VI  in 
the  morning ;  so  that  the  autumnal  equinox  was 
on  the  day  next  after  the  day  of  full  Moon. — The 
Dominical  letter  for  that  year  was  G,  and  conse- 
quently the  24th  of  October  was  on  a  Wednesday. 

*  The  reason  why  this  calculation  makes  the  autumnal 
equinox,  in  the  year  of  the  Julian  period  706,  to  be  two  days 
sooner  than  the  time  of  the  same  equinox  mentioned  in  page 
183,  is,  that  in  that  page  the  mean  time  only  is  taken  into 
the  account,  as  if  there  was  no  equation  of  the  Sun's  motion. 

The  equation  at  the  autumnal  equinox  then,  did  not  ex- 
ceed an  hour  and  a  quarter,  when  reduced  to  time  But,  in 
the  year  of  Christ  1756,  (which  was  5763  years  after,)  the 
equation  at  the  autumnal  equinox  amounted  to  1  cLy  22 
hours  24  minutes,  by  which  quantity  the  true  time  fell  later 
than  the  mean. — So  that  if  we  consider  the  true  time  of 
this  last-mentioned  equinox,  only  as  mean  time,  the  mean 
motion  of  the  Sun  carried  thence  back  to  the  autumnal 
equinox  in  the  year  of  the  Julian  period  706  will  fix  it  to 
the  25th  of  October  in  that  year. 


Concerning  Eclipses  of  the  Sun  and  Moon.  361 


To  find  the  Sun's  Distance  from  the  Moon's  ascend- 
ing Node,  at  the  1  me  oj  any  given  New  or  Full 
Moon  ;  and  consequently,  to  know  whether  there 
is  an  Eclifse  at  that  Time  or  not. 

The  Sun's  distance  from  the  Moon's  ascending- 
node  is  the  argument  for  finding  the  Moon's  fourth 
equation  in  the  syzygies,  and  therefore  it  is  taken 
into  all  the  foregoing  examples  in  finding  the 
times  of  these  phenomena. — 1  hus,  at  the  time  of 
mean  new  Moon  in  April  1764,  the  Sun's  mean 
distance  from  the  ascending  node  is  0s  5°  35'  2", 
See  Example  I.  p.  350. 

The  descending  node  is  opposite  to  the  ascend- 
ing one,  and  they  are,  therefore,  just  six  signs  dis- 
tant from  each  other. 

When  the  Sun  is  within  1 7  degrees  of  either  of 
the  nodes  at  the  time  of  new  Moon,  he  will  be 
eclipsed  at  that  time :  and  when  he  is  within  1 2 
degrees  of  either  of  the  nodes  at  the  time  of  full 
Moon,  the  Moon  will  be  then  eclipsed. — Thus  we 
find,  that  there  will  be  an  eclipse  of  the  Sun  at  the 
time  of  new  Moon  in  April  1764. 

But  the  true  time  of  that  new  Moon  comes  out 
by  the  equations  to  be  50  minutes  46  seconds  later 
than  the  mean  time  thereof,  by  comparing  these 
times  in  the  above  -example :  and  therefore,  we 
must  add  the  Sun's  motion  from  the  node  during 
that  interval  to  the.above  mean  distance  0s  5°  35'  2", 
which  motion  is  found  in  Table  XII,  for  50  mL- 
nutes  46  seconds,  to  be  2  12".  And  to  this  we 
must  apply  the  equation  of  the  Sun's  mean  distance 
from  the  node,  in  Table  XV,  found  by  the  Sun's 
anomaly,  which,  at  the  mean  time  of  new  Moon 
in  example  I,  is  9^  1  26'  19"  ;  and  then  we  shall 
have  the  Sun's  true  distance  from  the  node,  at  the 
true  time  of  new  Moon,  as  follows : 


-362  Elements  for  Solar  Eclipses. 

At  the  mean  time  of  new  Moon  in 


Sun  from  Node, 
s    o      /        // 


O  5  35     2 

Sun's  motion  from  the  7  50  minutes  2  1O 

node  for        —         3  46  seconds  2 

*  Sun's  mean  distance  from  node  at? 

•»yr  >          O      5       37        14 

true  new  Moon       —       —        3 
Equation  of  mean  distance  from?        950 
node,  add         —  3 

Sun's  true  distance  from  the  as- 


(    O  7   42  14 
cending  node       —         —         j 

which,  being  far  within  the  above  limit  of  1 7  de- 
grees, shews  that  the  Sun  must  then  be  eclipsed. 

And  now  we  shall  shew  how  to  project  this,  or 
any  other  eclipse,  either  of  the  Sun  or  Moon. 

To  project'  an  Eclipse  of  the  Sun. 

In  order  to  this,  we  must  find  the  ten  following 
elements  by  means  of  the  tables. 

1.  The  true  time  of  conjunction  of  the  Sun  and 
Moon ;  and  at  that  time,  2.  The  semidiameter  of 
the  Earth's  disc,  as  seen  from  the  Moon,  which  is 
equal  to  the  Moon's  horizontal  parallax.  3.  The 
Sun's  distance  from  the  solstitial  colure  to  which 
he  is  then  nearest.  4.  The  Sun's  declination. 
5.  The  angle  of  the  Moon's  visible  path  with  the 
ecliptic.  6.  The  Moon's  latitude.  7.  The  Moon's 
true  horary  motion  from  the  Sun.  8.  The  Sun's 
semidiameter.  9.  The  Moon's.  10.  The  semidia- 
meter of  the  penumbra. 

We  shall  now  proceed  to  find  these  elements 
for  the  Sun's  eclipse  in  April  1 764. 

To  find  the  true  time  of  new  Moon.  This,  by 
example  I,  p.  350,  is  found  to  be  on  the  first  day 
of  the  said  month,  at  3O  minutes  25  seconds  after 
X  in  the  morning. 


Elements  for  Solar  Eclipses.  '363 

2.  To  find  the  Moon's  horizontal  parallax,  or  sc- 
midtameter  of  the  Earth's  disc,  LS  sun  frc?n  the 
Moon.     Enter  Table  XVII,  with  tie  signs  and  de- 
grees of  the  Moon's  anomaly,  (making  proportions, 
because  the  anomaly  is  in  the  table  only  to  every 
6th  degree,)  and  thereby  take  out  the  Moon's  hori- 
zontal parallax;  which,  for  the  above  tiire,  answer- 
ing to  the  anomaly  1 1s  9°  24'  21  ,  is  54'  43". 

3.  To  find  the  Sun's  distance -jrom  the  nearest  sol- 
stice, 'viz.  the  beginning  of  Cancer,  iihich  is  3s  cr 
90  from  the  beginning  of  Aries.    It  appears  by  the 
example  on  page  358  (where  the  Sun's  place  is 
calculated  to  the  above  time  of  new  Moon)  that 
the  Sun's  longitude  from  the  beginning  of  Aries 
is  thenO5 12    10'  7'',  that  is,  the  Sun's  place  at  that 
time  is  r  Aries,  12°  1O'  7". 

s       o         /         n 

Therefore  from  3     O     O     0 

Subtract  the  Sun's  longitude  or  place  O  12     1O  7 

Remains  the  Sun's  distance  from  ?  _  0  -,  ^    .a  ro 

i_          i     •  c  —  <"    1  /    4*«-/    o  o 

the  solstice  <&          —  3 

Or  77°  49'  53":  each  sign  containing  30  degrees. 

4.  To  find  the  Sun's  delcination.     Enter  Table 
XIV,  with  the  signs  and  degrees  of  the  Sun's  true 
place,  viz.  Os  i  2°,  and  making  proportion  for  the 
1O'  7",  takeout  the  Sun's  declination  answering  to 
his  true  place,  and  it  will  be  found  to  be  4°  49' 
north. 

5.  To  find  the  Moon's  latitude.   This  depends  on 
her  distance  from  her  ascending  node,  which  is 
the  same  as  the  Sun's  distance  from  it  at  the  time 
of  new  Moon  :  and  with  this  the  Moon's  latitude 
is  found  in  Table  XVI. 

Now  we  have  already  found,  that  the  Sun's 
equated  distance  from  the  ascending  node,  at  the 
time  of  new  Moon  in  April  1764,  is  0s  7  42'  14". 
See  the  preceding  page. 

Therefore,  enter  Table  XVI,  with  O  sign  at  the 
top.  and  7  and  8  degrees  at  the  left  hand,  and  take 


The  Delineation  of  Solar  Eclipses. 

out  36'  and  39' ,  the  latitude  for  7°;  and  41'  51", 
the  latitude  for  8: :  and  by  making  pr  portion  be- 
tween these  latitudes  for  the  42'  14"  by  which  the 
Moon's  distance  from  the  node  exceeds  7  degrees ; 
her  true  latitude  will  be  found  to  be  40  18"  north- 
ascending. 

6.  'Lofind  the  Moon's  true  horary  motion  from  the 
Sun.  With  the  Moon's  anomaly,  viz.  ils  9    24' 
21",  enter  Table  XVII,  and  take  out  the  Moon's 
horary  motion ;  which,  by  making  proportion  in 
that  table,  will  be  found  to  be  30'  22".  Then,  with 
the  Sun's  anomaly,   9s   1°  26'  16",  take  out  his 
horary  motion  2  ,28'  from  the  same  table:  and 
subtracting  the  latter  from  the  former,  there  will 
remain  27  54"  for  the  Moon's  true  horary  motion 
from  the  Sun. 

7.  To  find  the  angle  of  the  Moon's  visible  path 
with  the  ecliptic.     This,  in  the  projection  of  eclip- 
ses, may  be  always  rated  at  5°  35  ,  without  any 
sensible  error. 

8,9.  To  find  the  semi  diameters  of  the  Sun  and 
Moon.  These  are  found  in  the  same  table,  and  by 
the  same  arguments,  as  their  horary  motions. — 
In  the  present  case,  the  Sun's  anomaly  gives  his 
semidiameter  16'  6",  ar.d  the  Moon's  anomaly 
gives  her  semidiameter  14'  57". 

1O.  To  find  the  semidiameter  of  the  -penumbra. 
Add  the  Moon's  semidiameter  to  the  Sun's,  and 
their  sum  will  be  the  semidiameter  of  the  penum- 
bra, viz.  31'  3' . 

Now  collect  these  elements,  that  they  may  be 
found  the  more  readily  when  they  are  wanted  in 
the  construction  of  this  eclipse. 

1 .  True  time  of  new  Moon  in  ~)    (1       1t      ,     K  , 

/I        •/    t^-r-A  (     *        •*"     °^      ^ 

April  1764          —  3  

6       •        /"'" 

2.  Semidiameter  of  the  Earth's  disc,     O  54  43 

3.  Sun's  dist.  from  the  nearest  solst.  77  49  53 

4.  Sun's  declination,  north  4  49     O 

5.  Moon's  latitude,  north-ascending    0  40  18 


The  Delineation  of  Solar  Eclipses, 


6.  Moon's  horary  motion  from  the  Sun  O  27  54 

7.  Angle  of  the  Moon's  visible? 

path  with  the  ecliptic          3 

8.  Sun's  semidiameter  16     6 

9.  Moon's  semidiameter  14  51 
10.  Semidiameter  of  the  penumbra  31     3 


To  project  an  Eclipse  of  the  Sun  geometrically. 

Make  a  scale  of  any  convenient  length,  as  AC,  Plate  xn, 
and  divide  it  into  as  many  equal  parts  as  the  Earth's  Fl£- L 
semi-disc  contains  minutes  of  a  degree ;  which,  at 
the  time  of  the  eclipse  in  April  1764,  is  54    43  '. 
Then,  with  the  whole  length  of  the  scale  as  a  ra- 
dius, describe  the  semicircle  ^fM^upon  the  centre 
C;  which  semicircle  shall  represent  the  northern 
half  of  the  Earth's  enlightened  disc,  as  seen  from 
the  Sun. 

Upon  the  centre  C  raise  the  straight  line  CH, 
perpendicular  to  the  diameter  ACE;  so  ACE  shall 
be  a  part  of  the  ecliptic,  and  CH  its  axis. 

Being  provided  with  a  good  sector,  open  it  to 
the  radius  CA  in  the  line  of  chords ;  and  taking 
from  thence  the  chord  of  23^-  degrees  in  your  com- 
passes, set  it  off  both  ways  from  //,  tog  and  to  b, 
in  the  periphery  of  the  semi-disc ;  and  draw  the 
straight  line  gVk9  in  which  the  north  pole  of  the 
disc  will  be  always  found. 

When  the  Sun  is  in  Aries,  Taurus,  Gemini,  Can- 
cer, Leo,  and  Virgo,  the  north  pole  of  the  Earth 
is  enlightened  by  the  Sun  :  but  while  the  Sun  is  in 
the  other  six  signs,  the  south  pole  is  enlightened, 
and  the  north  pole  is  in  the  dark. 

And  when  the  Sun  is  in  Capricorn,  Aquarius,Pis- 
ces,  Aries,  Taurus,  and  Gemini,  the  northern  half  of 
the  Earth's  axis  C  XII P  lies  to  the  right  hand  of  the 
axis  of  the  ecliptic,  as  seen  from  the  Sun ;  and  to 
the  left  hand,  while  the  Sun  is  in  the  other  six  signs. 

v 


368  The  Delineation  of  Solar  Eclipses, 

Open  the  sector  till  the  radius  (or  distance  of  the 
two  90' s)  of  the  signs  be  equal  to  the  length  of  Vb? 
and  take  the  sine  of  the  Sun's  distance  from  the 
solstice  (77°  49'  53')  as  nearly  as  you  can  guess, 
in  your  compasses,  from  the  line  of  sines,  and  set 
off  that  distance  from  V  to  P  in  the  line  gVh9  be- 
cause the  Earth's  axis  lies  to  the  right  hand  of  the 
axis  of  the  ecliptic  in  this  case,  the  Sun  being  in 
Aries ;  and  draw  the  straight  line  C  XII  P  for  the 
Earth's  axis,  of  which  P  is  the  north  pole.  If  the 
Earth's  axis  had  lain  to  the  left  hand  from  the  axis 
of  the  ecliptic,  the  distance  7P  would  have  been 
set  off  from  V  toward  g. 

To  draw  the  parallel  of  latitude  of  any  given  place, 
as  suppose  London,  or  the  path  of  that  place  on  the 
Earth's  enlightened  disc  as  seen  from  the  ^un,  from 
Sun-rise  till  Sun-set,  take  the  fallowing  method. 

Subtract  the  latitude  of  London,  51i°  from  90° 
and  the  remainder  38  \  will  be  the  co-latitude,  which 
take  in  your  compasses  from  the  line  of  chords, 
making  CA  or  CB  the  radius,  and  set  it  from  h 
(where  the  Earth's  axis  meets  :he  periphery  of  the 
disc)  to  VI  and  VI,  and  draw  the  occult  or  dotted 
line  VI  K  VI.  Then,  from  the  points  where  this 
line  meets  the  Earth's  disc,  set  off  the  chord  of 
the  Sun's  declination  4°  49'  to  D  and  F,  and  to  E 
and  G,  and  connect  these  points  by  the  two  occult 
lines  F  XII  G  and  OLE. 

Bisect  LK  XII  in  K,  and  through  the  point  K 
draw  the  black  line  VI  K  VI.  Then  making  CB 
the  radius  of  a  line  of  sines  on  the  sector,  take  the 
co-latitude  of  London  38 1"  from  the  sines  in  your 
compasses,  and  set  it  both  ways  from  K,  to  VI  and 
VI. — These  hours  will  be  just  in  the  edge  of  the 
disc  at  the  equinoxes,  but  at  no  other  time  in  tfte 
whole  year. 

With  the  extent  X"  VI,taken  into  your  compasses, 
set  one  foot  in  K  (in  the  black  line  below  the  occult 
one)  as  a  centre,  and  with  the  other  foot  describe  the 
semicircle  VI,  7,  8, 9,  1O,  &c.  and  divide  it  into  12 


The  Delineation  of  Solar  Eclipses.  367 

equal  parts.  Then  from  these  points  of  division, 
draw  the  occult  lines  7  p,  8,  o  n,  &c.  parallel  to  the 
Earth's  axis  C  XII  P. 

With  the  small  extent  ^XII  as  a  radius,  describe 
the  quadrantal  arc  XII yj  and  divide  it  into  six  equal 
parts,  as  XII  a,  ab,  be,  cd,  de,  and  ef\  and  through 
the  division- points,  a,  b,  c,  d,  e,  draw  the  occult 
lines  VII  e  V,  VIII  d  IV,  IX  c  III,  X  b  II,  and 
XI  a  I,  all  parallel  to  VI K  VI,  and  meeting  the  for- 
mer  occult  lines  7/>,  8  o,  &c.fin  thepoints  VII,  VIII, 
IX,  X,  XI,  V.  IV,  III,  II,  and  I:  which  points  shall 
mark  the  several  situations  of  London  on  the  Earth's 
disc,  at  these  hours  respectively,  as  seen  from  the 
Sun ;  and  the  elliptic  curve  VI  VII  VIII,  &c.  be- 
ing drawn  through  these  points  shall  represent  the 
parallel  of  latitude,  or  path  of  London  on  the  disc, 
as  seen  from  the  Sun,  from  its  rising  to  its  setting. 

A*.  B.  If  the  Sun's  declination  had  been  south, 
the  diurnal  path  of  London  would  have  been  on  the 
upper  side  of  the  line  VI  JTVI,  and  would  have 
touched  the  line  DLE  in  L.- — It  is  requisite  to  di- 
vide the  horary  spaces  into  quarters  (as  some  are  in 
the  figure)  and,  if  possible,  into  minutes  also* 

Make  CB,  the  radius  of  a  line  of  chord  on  the 
sector,  and  taking  therefrom  the  chord  of  5°  35', 
the  angle  of  the  Moon's  visible  path  with  the  eclip- 
tic, set  it  off  from  H  to  Mon  the  left  hand  of  CH> 
the  axis  of  the  ecliptic,  because  the  Moon's  latitude 
is  north-ascending.  Then  draw  CM  for  the  axis  of 
the  Moon's  orbit,  and  bisect  the  angle  MCffby  the 
right  line  Cz.-  Jf  the  Moon's  latitude  had  been  north- 
descending,  the  axis  of  her  orbit  would  have  been 
on  the  right  hand  from  the  axis  of  the  ecliptic. — 
A".  B.  The  axis  of  the  Moon's  orbit  lies  the  same 
way  when  her  latitude  is  south-ascending,  as  when 
it  is  north-ascending ;  and  the  same  way  when  south- 
descending,  as  when  north-descending. 

Take  the  Moon's  latitude  40'  18"  from  the  scale 
CA  in  your  compasses,  and  set  it  from  i  to  x  in  the 

3  A 


The  Delineation  of  Solar  Eclipses. 

bisecting  line  Cz,  making  ix  parallel  to  Cy :  and 
through  x,  at  right-angles  to  the  axis  of  the  Moon's 
orbit  CM,  draw  the  straight  line  N-wxy  S,  for  the 
path  of  the  penumbra's  centre  over  the  Earth's  disc. 
The  point  w  in  the  axis  of  the  Moon's  orbit,  is  that 
where  the  penumbra's  centre  approaches  nearest  to 
the  centre  of  the  Earth's  disc,  and  consequently  is 
the  middle  of  ihe  general  eclipse:  the  point  x  is  that 
where  the  conjunction  of  the  Sun  and  Moon  falls, 
according  to  equal  time  by  the  tables ;  and  the  p6int 
y  is  the  ecliptical  conjunction  of  the  Sun  and  Moon. 

Take  the  Moon's  true  horary  motion  from  the 
Sun,  27'  54",  in  your  compasses,  from  the  scale 
CA  (every  division  of  which  is  a  minute  of  a  de- 
gree), and  with  that  extent  make  marks  along  the 
path  of  the  penumbra's  centre;  and  divide  each  space 
from  mark  to  mark  into  sixty  equal  parts  or  horary 
minutes,  by  dots ;  and  set  the  hours  to  every  60th 
minute  in  such  a  manner,  that  the  dot  signifying  the 
instant  of  new  Moon  by  the  tables,  may  fall,  into  the 
point  x,  half  way  between  the  axis  of  the  Moon's 
orbit,  and  the  axis  of  the  ecliptic ;  and  then  the  rest 
of  the  dots  will  shew  the  points  of  the  Earth's  disc, 
where  the  penumbra's  centre  is  at  the  instants  de- 
noted by  them,  in  its  transit  over  the  Earth. 

Apply  one  side  of  a  square  to  the  line  of  the  pe- 
,  numbra's  path,  and  move  the  square  backward  and 
forward,  until  the  other  side  of  it  cuts  the  same 
hour  and  minute  (as  at  m  and  n)  both  in  the  path  of 
London,  and  in  the  path  of  the  penumbra's  centre : 
and  the  particular  minute  or  instant  which  the  square 
cuts  at  the  same  time  in  both  paths,  shall  be  the  in- 
stant of  the  visible  conjunction  of  the  Sun  and  Moon, 
or  greatest  obscuration  of  the  Sun,  at  the  place  for 
which  the  construction  is  made,  namely,  London, 
in  the  present  example ;  and  this  instant  is  at  47! 
minutes  past  X  o'clock  in  the  morning ;  which  is 
17  minutes  5  seconds  later  than  the  tabular  time  of 
true  conjunction. 


The  Delineation  of  Solar  Eclipses.  369 

Take  the  Sun's  semidiameter,  16'  6",  in  your 
compasses,  from  the  scale  CA,  and  setting  one  foot 
in  the  path  of  London  at  ;;z,  namely  at  47-|  minutes 
past  X,  with  the  other  foot  describe  the  circle  U\\ 
which  shall  represent  the  Sun's  disc  as  seen  from 
London  at  the  greatest  obscuration. — Then  take  the 
Moon's  semidiameter,  14'  57",  in  your  compasses, 
from  the  same  scale ;  and  setting  one  foot  in  the 
path  of  the  penumbra's  centre  at  m,  47-  minutes 
after  X ;  with  the  other  foot  describe  the  circle  TY 
for  the  Moon's  disc,  as  seen  from  London,  at  the 
time  when  the  eclipse  is  at  the  greatest ;  and  the 
portion  of  the  Sun's  disc  which  is  hid  or  cut  off  by 
the  Moon's,  will  shew  the  quantity  of  the  eclipse  at 
that  time ;  which  quantity  may  be  measured  on  a 
line  equal  to  the  Sun's  diameter,  and  divided  into 
12  equal  parts  for  digits. 

Lastly,  take  the  semidiameter  of  the  penumbra 
31'  3;/,  from  the  scale  CA  in  your  compasses;  and 
setting  one  foot  in  the  line  of  the  penumbra's  central 
path,  on  the  left  hand  from  the  axis  of  the  ecliptic, 
direct  the  other  foot  toward  the  path  tf  London ;  and 
carry  that  extent  backward  and  forward  till  both  the 
points  of  the  compasses  fall  into  the  same  instant  in 
both  the  paths ;  and  that  instant  will  denote  the  time 
when  the  eclipse  begins  at  London. — Then,  do  the 
like  on  the  right  hand  of  the  axis  of  the  ecliptic ;  and 
where  the  points  of  the  compasses  fall  into  the  same 
instant  in  both  the  paths,  that  instant  will  be  the 
time  when  the  eclipse  ends  at  London. 

These  trials  give  20  minutes  after  IX  in  the  morn- 
ing for  the  beginning  of  the  eclipse  at  London,  at  the 
points  A*  and  0;  47£  minutes  after  X,  at  the  points 
7/2  and  /?,  for  the  time  of  greatest  obscuration;  and  18 
minutes  after  XII,  at  R  and  S,  for  the  time  when 
the  eclipse  ends ;  according  to  mean  or  equal  time. 

From  these  times  we  must  subtract  the  equation 
of  natural  days,  viz.  3  minutes  48  seconds,  in  leap- 
year  April  1,  and  we  shall  have  the  apparent  times ; 


3  70  The  Delineation  of  Solar  Eclipses. 

namely,  IX  hours  16  minutes  12  seconds  for  the 
beginning  of  the  eclipse,  X  hours  43  minutes  42 
seconds  for  the  time  of  greatest  obscuration,  and 
XII  hours  14  minutes  12  seconds  for  the  time  when 
the  eclipse  ends. — But  the  best  way  is  to  apply  this 
equation  to  the  true  equal  time  of  new  Moon,  before 
the  projection  be  begun ;  as  is  done  in  example  I. 
For  the  motion  or  position  of  places  on  the  Earth's 
disc  answers  to  apparent  or  solar  time. 

In  this  construction,  it  is  supposed  that  the  angle 
under  which  the  Moon's  disc  is  seen,  during  the 
whole  time  of  the  eclipse,  continues  invariably  the 
same  and  that  the  Moon's  motion  is  uniform  and 
rectilinear  during  that  time. — But  these  suppositions 
do  not  exactly  agree  with  the  truth ;  and  therefore, 
supposing  die  elements  given  by  the  tables  to  be  ac- 
curate, yet  the  times  and  phases  of  the  eclipse,  de- 
duced from  its  construction,  will  not  answer  exactly 
to  what  passes  in  the  heavens ;  but  may  be  at  least 
two  or  three  minutes  wrong,  though  done  with  the 
greatest  care.- — Moreover,  the  paths  of  all  places  of 
considerable  latitudes  are  nearer  the  centre  of  the 
Earth's  disc,  as  seen  from  the  Sun,  than  those  con- 
structions make  diem ;  because  the  disc  is  projected 
as  if  the  Earth  were  a  perfect  sphere,  although  it  is 
known  to  be  a  spheroid.  Consequently,  the  Moon's 
shadow  will  go  farther  northward  in  all  places  of 
northern  latitude,  and  farther  southward 'in  all  places 
of  southern  latitude,  than  it  is  shewn  to  do  in  these 
projections. — According  to  Mayer^s  tables,  this 
eclipse  will  be  about  a  quarter  of  an  hour  sooner 
than  either  these  tables,  or  Mr.  Flamstead's,  or  Dr. 
Halley^,  make  it :  and  Mayer's  tables  do  not  make 
it  annular  at  London, 


The  Delineation  of  Lunar  Eclipses. 

The  projection  qfLiyar  Eclipses. 

When  the  Moon  is  within  12  degrees  of  either  oi 
her  nodes,  at  the  time  when  she  is  full,  she  will  be 
eclipsed,  otherwise  not. 

We  find  by  example  II.  page  351,  that  at  the 
time  of  mean  full  Moon  in  May,  1762,  the  Sun's 
distance  from  the  ascending  node  was  only  4°  49' 
35'',  and  the  Moon  being  then  opposite  to  the  Sim, 
must  have  been  just  as  near  her  descending  node, 
and  was  therefore  eclipsed. 

The  elements  for  constructing  an  eclipse  of  the 
Moon  are  eight  in  number,  as  follows : 

1.  The  true  time  of  full  Moon  :  and  at  that  time. 
2.  The  Moon's  horizontal  parallax.  3.  The  Sun's 
semidiameter.  4.  The  Moon's.  5.  The  semidia- 
meter of  the  Earth's  shadow  at  the  Moon.  6.  The 
Moon's  latitude.  7.  The  angle  of  the  Moon's  visi- 
ble path  with  the  ecliptic.  8.  The  Moon's  true 
horary  motion  from  the  Sun. — Therefore, 

1.  To  find  the  true  time  of  full  Moon.  Work  af« 
already  taught  in  the  precepts. — Thus  we  have  tlte 
true  time  of  full  Moon  in  May,  1762,  (see  exam- 
ple II.  page  351,)  on  the  8th  day,  at  50  minutes  50 
seconds  past  III  o'clock  in  the  morning. 

2.  To  find  the  Moon's  horizontal  parallax.  Enter 
Table  XVII.  with  the  Moon's  mean  anomaly  (at 
the  above  full)  98  2°  42'  42",  and  thereby  take  out 
her  horizontal  parallax ;  which  by  making  the  re- 
quisite proportion,  will  be  found  to  be  57'  20". 

3.  4.     To  find  the  semidiameter  s  of  the  Sun  and 
Moon.     Enter  Table  XVII,  with  their  respective 
anomalies,  the  Sun's  being  10s  7°  27'  45"  (by  the 
above  example),  and  the  Moon's  9s  2°  42'  42" ;  and 
thereby  take  out  their  respective  semidiameters :  the 
Sun's  15'  56",  and  the  Moon's  15'  39". 

5.  To  find  the  semidiameter  of  tJie  Earth'' s  sha- 
dow at  the  Moon.  Add  the  Sun's  horizontal  paraU 


372  The  Delineation  of  Lunar  Eclipses. 

lax,  which  is  always  10",  to  the  Moon's,  which  in/ 
the  present  case  is  57' 20",  the  sum  will  be  57'  30", 
from  which  subtract  the  Sun's  semidiamcter  15'  56", 
and  there  will  remain  41'  34"  for  the  semidiameter 
of  that  part  of  the  Earth's  shadow  which  the  Moon 
then  passes  through. 

6.  To  find  the  Momti  latitude.  Find  the  Sun's 
true  distance  from  the  ascending  node  (as  already 
taught  in  page  361)  at  the  true  time  of  full  Moon ; 
and  this  distance,  increased  by  six  signs,  will  be  the 
Moon's  true  distance  from  the  same  node ;  and  con- 
sequently the  argument  for  finding  her  true  latitude* 
as  shewn  in  page  363. 

Thus,  in  example  II.  the  Sun's  mean  distance 
from  the  ascending  node  was  0s  4°  49'  35",  at  the 
time  of  mean  full  Moon  :  but  it  appears  by  the  ex- 
ample, that  the  true  time  thereof  was  6  hours  33 
minutes  38  seconds  sooner  than  the  mean  time,  and 
therefore  we  must  subtract  the  Sun's  motion  from 
the  node  (found  in  Table  XII,  page  342)  during 
this  interval,  from  the  above  mean  distance  0s  4°  49' 
35",  in  order  to  have  his  mean  distance  from  it  at 
the  true  time  of  full  Moon. — Then  to  this  apply  the 
equation  of  his  mean  distance  from  the  node  found 
in  Table  XV.  by  his  mean  anomaly  10s  7°  27'  45"; 
and  lastly,  add  six  signs  :  so  shall  the  Moon's  true 
distance  from  the  ascending  node  be  found  as 
follows : 

s        O       /          // 

Sun  from  node  at  mean  full  Moon        0    4  49  35 


C    6  hours  15  35 

His  motion  from  it  in    <  33  minutes  1  26 

r  38  seconds 


Sum,  subtract  from  the  uppermost  line          17    3 
Remains  his  mean  distance  at  true  ? 


full  Moon        —  3 


0  4  32  32 


The  Delineation  of  Lunar  Eclipses.  373 

s         O       f  H 

Equation  of  his  mean  distance,  add     0     1  38    0 

'    «  i    i  -ii 

Sun's  true  distance  from  the  node        0    6  10  32 
To  which  add  6000 

And  the  sum  will  be  6     6  10  32 

which  is  the  Moon's  true  distance  from  her  as- 
cending node  at  the  true  time  of  her  being  full ;  and 
consequently  the  argument  for  finding  her  true  lati- 
tude at  that  time. — Therefore,  with  this  argument, 
enter  Table  XVI.  making  proportion  between  the 
latitudes  belonging  to  the  6th  and  7th  degree  of  the 
argument  at  the  left  hand  (the  signs  being  at  the 
top)  for  the  10'  32",  and  it  will  give  32'  21"  for  the 
Moon's  true  latitude,  which  appears  by  the  table  to 
be  south-descending. 

7.  To  find  the  angle  of  the  Moon's  visible  path 
-with  the  ecliptic.     This  may 'be  stated  at  5°  35', 
without  any  error  of  consequence  in  the  projection 
of  the  eclipse. 

8.  To  find  the  Moon's  true  horary  motion  from 
the  Sun.    With  their  respective  anomalies  take  out 
their  horary  motions  from  Table  XVII.  in  page  346; 
and  the  Sun's  horary  motion  subtracted  from  the 
Moon's,  leaves  remaining  the  Moon's  true  horary 
xnotion  from  the  Sun :  in  the  present  case  30'  52". 

Now  collect  these  elements  together  for  use. 


D.  H.  M.  S. 

1.  True  time  of  full  Moon  in 
May,  1762 


8     3  50  50 


2.  Moon's  horizontal  parallax-  0  57  20 

3.  Sun's  semidiameter  0  15  56 

4.  Moon's  semidiameter  *     0  15  39 

5.  Semidiameter  of  the  Earth's  shadow")    A   .,,   *  * 
at  the  Moon  T  °  41  °4 


374  The  Delineation  of  Lunar  Eclipses. 

O        I          If 

6.  Moon's  true  latitude,  south-descending  0  32  21 

7.  Angle  of  her  visible  path  with  the ")  *"    -  Q  t 
ecliptic  J 

8.  Her  true  horary  motion  from  the  Sun    0  30  52 

Plate  XIL  These  elements  being  found  for  the  construction 
of  the  Moon's  eclipse  in  May  1762,  proceed  as 
follows : 

Fig.  II.  Make  a  scale  of  any  convenient  length,  as  W Jf, 
and  divide  it  into  60  equal  parts,  each  part  standing 
for  a  minute  of  a  degree. 

Draw  the  right  line  ACE  (Fig.  3.)  for  part  of 
the  ecliptic,  and  CD  perpendicular  to  it  for  the 
southern  part  of  its  axis ;  the  Moon  having  south 
latitude. 

Add  the  semidiameters  of  the  Moon  and  Earth's 
shadow  together,  which,  in  this  ellipse,  will  make 
57'  13" ;  and  take  this  from  the  scale  in  your  com- 
passes, and  setting  one  foot  in  the  point  C,  as  a  cen- 
tre, with  the  other  foot  describe  the  semicircle 
AD B ;  in  one  point  of  which  the  Moon's  centre 
will  be  at  the  beginning  of  the  eclipse,  and  in  an- 
other at  the  end  of  it. 

Take  the  semidiameter  of  the  Earth's  shadow, 
41'  34",  in  your  compasses  from  the  scale,  and  set- 
ting one  foot  in  the  centre  C,  with  the  other  foot  de- 
scribe the  semicircle  KLM  for  the  southern  half 
of  the  Earth's  shadow,  because  the  Moon's  latitude 
is  south  in  this  eclipse. 

Make  C  D  the  radius  of  a  line  of  chords  on  the 
sector,  and  set  oft'  the  angle  of  the  Moon's  visi- 
ble path  with  the  ecliptic,  5°  35',  from  D  to  E,  and 
draw  the  right  line  C  FE  for  the  southern  half  of 
the  axis  of  the  Moon's  orbit,  lying  to  the  right  hand 
from  the  axis  of  the  ecliptic  CZ),  because  the  Moon's 
latitude  is  south- descending. — It  would  have  been 
the  same  way  (on  the  other  side  of  the  ecliptic)  if 
her  latitude  had  been  north- descending;  but  contrary 


The  Delineation  of  Lunar  Eclipses.  375 

m  both  cases,  if  her  latitude  had  been  either  north- 
ascending  or  south-ascending. 

Bisect  the  angle  D  C  E  by  the  right  line  C  g,  in 
which  line  the  true  equal  time  of  opposition  of  the 
Sun  and  Moon  falls,  as  given  by  the  tables. 

Take  the  Moon's  latitude,  32'  21",  from  the  scale 
with  your  compasses,  and  set  it  from  CYto  G,  in  the 
line  C  G  g ;  and  through  the  point  G,  at  right  an- 
gles to  CF  E,  draw  the  right  line  P  H  G  F  JV  for 
the  path  of  the  Moon's  centre.  Then  F  shall  be 
the  point  in  the  Earth's  shadow,  where  the  Moon's 
centre  is  at  the  middle  of  the  eclipse ;  G,  the  point 
where  her  centre  is  at  the  tabular  time  of  her  be- 
ing full ;  and  H,  the  point  where  her  centre  is  at  the 
instant  of  her  ecliptical  opposition. 

Take  the  Moon's  horary  motion  from  the  Sun,  30' 
52",  in  your  compasses  from  the  scale ;  and  with 
that  extent  make  marks  along  the  line  of  the  Moon's 
path,  P  G  N:  Then  divide  each  space  from  mark 
to  mark,  into  60  equal  parts,  or  horary  minutes,  and 
set  the  hours  to  the  proper  dots  in  such  a  manner, 
that  the  dot  signifying  the  instant  of  full  Moon,  (viz. 
50  minutes  50  seconds  after  III  in  the  morning) 
may  be  in  the  point  G,  where  the  line  of  the  Moon's 
path  cuts  the  line  that  bisects  the  angle  D  C  E. 

Take  the  Moon's  semidiameter,  15'  39",  ia 
your  compasses  from  the  scale,  and  with  that  ex- 
tent, as  a  radius,  upon  the  points  JV,  F,  and  P,  as 
centres,  describe  the  circle  Q  for  the  Moon  at  the 
beginning  of  the  eclipse,  when  she  touches  the 
Earth's  shadow  at  F ' ;  the  circle  R  for  the  Moon  at 
the  middle  of  the  eclipse  ;  and  the  circle  S  for  the 
Moon  at  the  end  of  the  eclipse,  just  leaving  the 
Earth's  shadow  at  17. 

The  point  N  denotes  the  instant  when  the  eclipse- 
begins,  namely,  at  15  minutes  10  seconds  after  II 
in  the  morning ;  the  point  F  the  middle  of  the 
eclipse,  at  47  minutes  45  seconds  past  III ;  and 
the  point  P  the  end  of  the  eclipse,  at  18  minutes 
after  V. — At  the  greatest  obscuration  the  Moon  is. 
10  digits  eclipsed.  3  B 


376  An  ancient  Edipse'of  the  Moon  described. 


Concerning  an  ancient  Eclipse  of  the  Moon. 

It  is  recorded  by  Ptolemy,  from  Hipparclws, 
that  on  the  22d  of  September,  the  year  201  before 
the  first  year  of  Christ,  the  Moon  rose  so  much 
eclipsed  at  Alexandria,  that  the  eclipse  must  have 
begun  about  half  an  hour  before  she  rose. 

Mr.  Carey  puts  down  the  eclipse  in  his  Chrono- 
logy as  follows,  among  several  other  ancient  ones,, 
recorded  by  different  authors : 


Jul.  Per. 


451 


Sept.  22. 


Eel.  •/>«-.  Gz/#i."  2  An.  54.  Hor.  7. 

P.  M.  Alexandr.  Dig.  eccl.  10. 

[Ptolem.  I.  4.  c.  11.] 


Nadonassar. 

547. 
Mesor.  16. 


That  is,  in  the  45  L3th  year  of  the  Julian  period, 
which  was  the  547th  year  from  Nabonassar,  and 
the  54th  year  of  the  second  Calif  ic  period,  on  the 
16th  day  of  the  month  Mesori,  (which  answers  to 
the  22d  of  September  J  the  Moon  was  10  digits 
eclipsed  at  Alexandria,  at  7  o'clock  in  the  evening. 

Now,  as  our  Saviour  was  born  (according  to  the 
Dionysianor  vulgar  sera  of  his  birth)  in  the  4713th 
year  of  the  Julian  period,  it  is  plain  that  the  4513th 
year  of  that  period  was  the  200th  year  before  the 
year  of  Christ's  birth ;  and  consequently  201  years 
before  the  year  of  Christ  1. 

And  in  the  year  201,  on  the  22d  of  September, 
it  appears  by  example  V.  (page  354)  that  the  Moon 
was  full  at  26  minutes  28  seconds  past  VII  in  the 
evening,  in  the  meridian  of  Alexandria. 

At  that  time,  the  Sun's  place  was  Virgo  26°  14', 
according  to  our  tables  ;  so  that  the  Sun  was  then 
within  4  degrees  of  the  autumnal  equinox ;  and  ac- 
cording to  calculation  he  must  have  set  at  Alexan- 
dria about  5  minutes  after  VI,  and  about  one  de- 
gree north  of  the  west. 

The  Moon  being  full  at  that  time,  would  have  risen 
just  at  Sun- set,  about  one  degree  south  of  the  east, 


An  ancient  Eclipse  of  the  Moon  described.  377 

jf  she  had  been  in  either  of  her  nodes,  and  her  visi- 
ble place  not  depressed  by  parallax. 

But  her  parallactic  depression  (as  appears  from 
her  anomaly,  viz.  109  6°  nearly)  must  have  been 
55'  17" ;  which  exceeded  her  whole  diameter  by 
24'  53"  ;  but  then,  she  must  have  been  elevated  33' 
45"  by  refraction;  which,  subtracted  from  her 
parallax,  leaves  21'  32"  for  her  visible  or  apparent 
depression. 

And  her  true  latitude  was  30£  north-descending, 
which  being  contrary  to  her  apparent  depression, 
and  greater  than  the  same  by  8'  58",  her  true  time 
of  rising  must  have  been  just  about  VI  o'clock. 
Now,  as  the  Moon  rose  about  one  degree  south  of 
the  east  at  Alexandria,  where  the  visible  horizon  is 
land,  and  not  sea,  we  can  hardly  imagine  her  to  have 
been  less  than  15  or  20  minutes  of  time  above  the 
true  horizon  before  she  was  visible. 

It  appears  by  Fig.  4,  which  is  a  delineation  of  this 
eclipse  reduced  to  the  time  at  Alexandria,  that  the 
eclipse  began  at  53  minutes  after  V  in  the  evening  ^ 
and  consequently  7  minutes  before  the  Moon  was  in 
the  true  horizon  ;  to  which  if  we  add  20  minutes, 
for  the  interval  between  her  true  rising  and  her  be- 
ing visible,  we  shall  have  27  minutes  for  the  time 
that  the  eclipse  was  begun  before  the  Moon  was  vi- 
sibly risen.  The  middle  of  this  eclipse  was  at  30 
minutes  past  VII,  when  its  quantity  was  almost  10 
digits,  and  its  ending  was  at  6  minutes  past  IX  in 
the  evening.  So  that  our  tables  come  as  near  to 
the  recorded  time  of  this  eclipse  as  can  be  expect- 
ed, after  an  elapse  of  1960  years. 


37$  Of  thefxed  Stars. 

CHAP.  XVJIL 

Of  thefxed  Stars. 

toSltaCrs354  T^HE  Stars  are  said  to  be  fixed,  because 
appear  "  '  J_  they  have  been  generally  observed  to 
bigger  keep  at  the  same  distances  from  each  other,  their 
viewed  apparent  diurnal  revolution  being  caused  solely  by 
by  the  the  Earth's  turning  on  its  axis.  They  appear  of  a 
than  when  sensible  magnitude  to  the  bare  eye,  because  the 
seen  retina  is  affected  not  only  by  the  rays  of  light 
through  whjch  are  emitted  directly  from  them,  but  by 

a  tele-  J.  .   ,     r   ..  J 

scope.      many  thousands   more,    which  falling   upon   our 

eye-lids,   and  upon  the  aerial  particles  about  us, 

are  reflected  into  our  eyes  so  strongly,  as  to  excite 

vibrations  not   only  in  those  points  of  the   retina 

where  the  real  images  of  the  stars  are  formed,  but 

also  in  other  points  at  some  distance  round  about. 

This  makes  us  imagine  the  stars  to  be  much  bigger 

than  they  would  appear,  if  we  saw  them  only  by  the 

few  rays  coming  directly  from  them,  so  as  to  enter 

our  eyes  without  being  intermixed  with  others.  Any 

one  may  be  sensible  of  this,  by  looking  at  a  star  of 

the  first  magnitude  through  a  long  narrow  tube ; 

which,  though  it  takes  in  as  much  of  the  sky  as 

would  hold  a  thousand  such  stars,  it  scarce  renders 

that  one  visible. 

The  more  a  telescope  magnifies,   the  less  is  the 
'aperture  through  which  the  star  is  seen  ;  and  con- 
A  proof    sequently  the  fewer  rays  it  admits  into  the  eye.  Now 
that  they   since  the  stars  appear  less  in  a  telescope  which  mag- 
their  own  nifies  200  times,  than  they  do  to  the  bare  eye,  inso- 
much  that  they  seem  to  be  only  indivisible  points, 
it  proves  at  once  that  the  stars  are  at  immense  dis- 
tances from  us,   and  that  they  shine  by  their  own 
proper  light.      If  they  shone   by   borrowed   light, 
the}-  would  be  as  invisible  without  telescopes  as  the 
satellites  of  Jupiter  are ;  for  these  satellites  appear 


Of  the  fixed  Stars.  379 

bigger  when  viewed  with  a  good  telescope  than  the 
largest  fixed  stars  do. 

355.  The  number  of  stars  discoverable  in  ei- 
ther hemisphere,  by  the  naked  eye,  is  not  above  a 
thousand.     This  at  first  may  appear  incredible,  be- 
cause they  seem  to  be  without  number :  but  the  de- Their 
ception  arises  from  our  looking  confusedly  wp°n  m^hTess 
them,  without  reducing  them  into  any  order.   For  than  is 
look  but  stedfastly  upon  a  pretty  large  portion  of  the  f^-jf^ 
sky,  and  count  the  number  of  stars  in  it,  and  you 
will  be  surprised  to  find  them  so  few.     And,  if  one 
considers  how  seldom  the  Moon  meets  with  any 
stars  in  her  way,  although  there  are  as  many  about 
her  path  as  in  other  parts  of  the  heavens,  he  will 
soon  be  convinced  that  the  stars  are  much  thinner 
sown  than  he  was  aware  of.  The  British  catalogue, 
which,  besides  the  stars  visible  to  the  bare  eye,  in- 
cludes a  great  number  which  cannot  be  seen  with- 
out the  assistance  of  a  telescope,  contains  no  more 
than  3000  in  both  hemispheres. 

356.     As  we  have  incomparably  more  light  from  The  ab- 
the  Moon  than  from  all  the  stars  together,  it  is  the  *^£> ling- 
greatest  absurdity  to  imagine  that  the  stars  were  the  stars 
made  for  no  other  purpose  than  to  cast  a  faint  light  ^®  onlv 
upon  the  Earth  :  especially  since  many  more  require  to  shine  " 
the  assistance  of  a  good  telescope  to  find  them  out,  "P°£  us 
than  are  visible  without  that  instrument.     Our  Sun  night, 
is  surrounded  by  a  system  of  planets  and  comets  ; 
all  of  which  would  be  invisible  from  the  nearest 
fixed  star.     And  from  what  we  already  know  of  the 
immense  distance  of  the  stars,  the  nearest  may  be 
computed  at  32,000,000,000,000  of  miles  from  us, 
which  is  further  than  a  cannon-ball  would  fly  in 
7,000,000  of  years.      Hence  it  is  easy  to  prove, 
that  the  Sun,  seen  from  such  a  distance,  would  ap- 
pear no  bigger  than  a  star  of  the  first  magnitude. 
From  all  this  it  is  highly  probable  that  each  star  is  a 
Sun  to  a  system  of  worlds  moving  round  it,  though 
unseen  by  us ;  especially  as  the  doctrine  of  plurali- 
ty of  worlds  is  rational,  and  greatly  manifests  the 
Power,  Wisdom,  and  Goodness  of  the  Great  Cre- 
ator. 


380  Of  the  fixed  Stars. 

Their  dif-  357.  The  stars,  on  account  of  their  apparently 
maTi  vari°us  magnitudes,  have  been  distributed  into  se- 
tudes :  veral  classes  or  orders.  Those  which  appear  larg- 
est, are  called  st'ars  of  the  first  magnitude ;  the 
next  to  them  in  lustre,  stars  of  the  second  magni- 
tude;  and  so  on  to  the  sixth  ;  which  are  the  small- 
est that  are  visible  to  the  bare  eye.  This  distribu- 
tion having  been  made  long  before  the  invention  of 
telescopes,  the  stars  which  cannot  be  seen  without 
the  assistance  of  these  instruments,  are  distinguish- 
ed by  the  name  of  telescopic  stars. 

And  dlvi-       358.  The  ancients  divided  the  starry  sphere  into 
coMtetta-  Particular  constellations,  or   systems  of  stars,   ac- 
tions,       cording  as  they  lay  near  one  another,  so  as  to  occu- 
py those  spaces  with  the  figures  of  different  sorts  of 
animals  or  things  would  take  up,  if  they  were  there 
delineated.    And  those  stars  which  could  not  be 
brought  into  any  particular  constellation,  were  called 
unformed  stars. 

The  use  ^59.  This  division  of  the  stars  into  different  con- 
of  this  di-  stellations  or  asterisms,  serves  to  distinguish  them 
vision.  from  one  another,  so  that  any  particular  star  may 
be  readily  found  in  the  heavens  by  means  of  a  ce- 
lestial globe ;  on  which  the  constellations  are  so  de- 
lineated as  to  put  the  most  remarkable  stars  into 
such  parts  of  the  figures  as  are  most  easily  distin- 
guished. The  number  of  the  ancient  constella- 
tions is  48,  and  upon  our  present  globes  about  70. 
On  Senex's  globes,  Bayer's  letters  are  inserted ; 
the  first  in  the  Greek  alphabet  being  put  to  the  big- 
gest star  in  each  constellation,  the  second  to  the 
,  next%  and  so  on  :  by  which  means,  every  star  is  as 
easily  found  as  if  a  name  were  given  to  it.  Thus, 
if  the  star  v  in  the  constellation  of  the  Ram  be 
mentioned,  every  astronomer  knows  as  well  what 
star  is  meant,  as  if  it  were  pointed  out  to  him  in  the 
heavens. 

The  zodi-     360.  There  is  also  a  division  of  the  heavens  into 

ac"          three    parts,     1.   The   zodiac    (£*r/**cf)    from   fWicv 

zodion  an  animal,  because  most  of  the  constellations 

in  it,  which  are  twelve  in  number,  are  the  figures  of 


Of  the  fixed  Stars.  381 

animals :  as  Aries  the  Ram,  Taurus  the  Bull,  Ge- 
mini the  twins,  Cancer  the  Crab,  Leo  the  Lion, 
Virgo  the  Virgin,  Libra  the  Balance,  Scorpia  the 
Scorpion,  Sagittarius  the  Archer,  Capricornus  the 
Goat,  Aquarius  the  Water-bearer,  and  Pisces  the 
Fishes.  The  zodiac  goes  quite  round  the  heavens  : 
it  is  about  16  degrees  broad,  so  that  it  takes  in  the 
orbits  of  all  the  planets,  and  likewise  the  orbit  of  the 
Moon.  Along  the  middle  of  this  zone  or  belt  is  the 
ecliptic,  or  circle  which  the  Earth  describes  annually 
as  seen  from  the  Sun  ;  and  which  the  Sun  appears 
to  describe  as  seen  from  the  Earth.  2.  All  that  re- 
gion of  the  heavens,  which  is  on  the  north  side  of 
the  zodiac,  containing  21  constellations.    And,  3d, 
That  on  the  south  side,  containing  15. 

361.  The  ancients  divided  the  zodiac  into  the  The  man- 
above  12  constellations  or  signs  in  the  folio  wing  "UJf^J" 
manner.  They  took  a  vessel  with  a  small  hole  in  by  the  an- 
the  bottom,  and  having  filled  it  with  water,  suffered 
the  same  to  distil  drop  by  drop  into  another  vessel 
set  beneath  to  receive  it ;  beginning  at  the  moment 
when  some  star  rose,  and  continuing  until  it  rose  the 
next  following  night.  The  water  falling  down  into 
the  receiver,  they  divided  into  twelve  equal  parts  ; 
and  having  two  other  small  vessels  in  readiness,  each 
of  them  fit  to  contain  one  part,  they  again  poured  all 
the  water  into  the  upper  vessel,  and,  observing  the 
rising  of  some  star  in  the  zodiac,  they  at  the  same 
time  suffered  the  water  to  drop  into  one  of  the  small 
vessels ;  and  as  soon  as  it  was  full,  they  shifted  it, 
and  set  an  empty  one  in  its  place.  When  each  ves- 
sel was  full,  they  took  notice  what  star  of  the  zodiac 
rose ;  and  though  this  could  not  be  done  in  one 
night,  yet  in  many  they  observed  the  rising  of  twelve 
stars  or  points,  by  which  they  divide  the  zodiac  into 
twelve  parts. 


382 


Of  the  fixed  Stars. 


362.  The  names  of  the  constellations  and  the  number  of 
stars  observed  in  each  of  them  by  different  astronomers,  are 
as  follows  : 


The  ancient  Constellations.                                       Ptolemy.  Tycho.  Hevcl  Flamst. 

Ursa  minor                         The  Little  Bear                        712       24 

Ursa  major 

The  Great  Bear 

35 

29 

73 

87 

Draco 

The  Dragon 

31 

32 

40 

80 

Cepheus 

Cepheus 

13 

4 

51 

35 

Bootes,  Arctofihilax 

23 

18 

52 

54 

Corona  Borealis 

The  Northern  Crown 

8 

8 

8 

21 

Hercules,  En-gonaszn 

Hercules  kneeling 

29 

28 

45 

113 

Lyra 

The  Harp 

10 

11 

17 

21 

Cygnus,  Gallina 

The  Swan 

19 

18 

47 

81 

Cassiopea 

The  Lady  in  her  Chair 

13 

26 

47 

55 

Perseus 

Perseus 

29 

29 

46 

59 

Auriga 

The  Waggoner 

14 

9 

40 

66 

Serpentarius,  Ofthiuchus 

Serpentarius 

29 

15 

40 

74 

Serpens 

The  Serpent 

18 

13 

22 

64 

Sagitta 

The  Arrow 

5 

5 

5 

IS 

Aquila,  Vultur 

The  Eagle  > 

I 

\  12 

23) 

Antinous 

Antinous     $ 

i 

I    3 

19$ 

Delphinus 

The  Dolphin 

10 

10 

14 

18 

Equulus,  Equi  sectio 

The  Horse's  Head 

4 

4 

6 

10 

Pegasus,  Equus 

The  Flying  Horse 

20 

19 

38 

89 

Andromeda 

Andromeda 

23 

23 

47 

66 

Triangulum 

The  Triangle 

4 

4 

12 

16 

Aries 

The  Ram 

18 

21 

27 

66 

Taurus 

The  Bull 

44 

43 

51 

141 

Gemini 

The  Twins 

25 

25 

38 

85 

Cancer 

The  Crab 

23 

15 

29 

83 

Leo 

The  Lion            > 

f  30 

49 

95 

Coma  Berenices 

Berenice's  Hair  5 

35 

£  14 

21 

43 

Virgo 

The  Virgin 

32 

33 

50 

110 

Libra,  Chela 

The  Scales 

17 

10 

20 

51 

Sc6rpius 

The  Scorpion 

24 

10 

20 

44 

Sagittarius 

The  Archer 

31 

14 

22 

69 

Capricornus 

The  Goat 

28 

28 

29 

51 

Aquarius 

The  Water-Bearer 

45 

41 

47 

108 

Pisces 

The  Fishes 

38 

36 

39 

113 

Cetus 

The  Whale 

22 

21 

45 

97 

Orion 

Orion 

38 

42 

62 

78 

Eridanus,  Fluvius 

Eridanus,  the  River 

34 

10 

27 

84 

Lepus 

The  Hare 

12 

13 

16 

J9 

Canis  major 

The  Great  Dog 

29 

13 

'  21 

31 

Canis  minor 

The  Little  Dog 

2 

2 

13 

14 

Of  the  fixed  Stars.  383 


The  ancient  Constellations.                          Ptolemy.  Tycho. 

HtveLFlamst. 

Aro-o                                  The  Ship                          45       3 

4 

64 

Hydra                                  The  Hydra                        27     19 

31 

60 

Crater                                 The  Cup                             7       3 

10 

Si 

Corvtis                                The  Crow                           7       4 

9 

Centaurus                          The  Centaur                    S7 

35 

Lupus                                The  Wolf                         19 

24 

Ara                                    The  Altar                           7 

9 

Corono  Australia              The  Southern  Crown      13 

12 

Piscis  Australis                The  Southern  Fish           18 

24 

The  New  Southern  Constellations. 

Columba  Naochi                 Noah's  Dove 

LO 

llobur  Carolinum                The  Royal  Oak 

12 

Grus                                       The  Crane 

13 

Phoenix                                 The  Phenix 

13 

Indus                                      The  Indian 

12 

Pavo                                       The  Peacock 

14 

Apus,  A-viz  Indica             The  Bird  of  Paradise 

11 

Apis,  Musca                        The  Bee  or  Fly 

4 

Chamaeleon                         The  Chameleon 

10 

Triangulum  Australis       The  South  Triangle 

5 

Piscis  volans,  Passer         The  Flying  Fish 

8 

Dorado,  Xiphias                 The  Sword  Fish 

6 

Toucan                                The  American  Goose 

9 

Hydrus                                The  Water  Snake 

10 

Hevelius's  Constellations  made  out  of  the  unformed 

Stars. 

Jfevelius. 

Flamst. 

Lynx                                 The  Lynx 

19 

44 

Leo  minor                        The  Little  Lion 

53 

Asteron  Sc  Chara             The  Greyhounds 

23 

25 

Cerberus                           Cerberus 

4 

Vulpecula  Sc  Anser         The  Fox  and  Goose 

27 

35 

Scutum  Sobieski             Sobieski's  Shield 

7 

Lacerta                             The  Lizard 

16 

CameiOpardalus               The  Camelopard 

32 

58 

Monoceros                        The  Unicorn 

19 

3l 

Sextans                            The  Sextant 

11 

41 

363.  Ther,e  is  a  remarkable  track  round  the  hea- 
•  vens,  called  the  Milky  Way,  fr(  m  its  peculiar  white- 
ness, which  is  found,  by  means  of  the  telescope,  to 
be  owing  to  a  vast  number  of  very  small  stars,  that 

3  C 


384  Of  Lucid  Spots  in  the  Heavens. 

are  situate  in  that  part  of  the  heavens.    This  track 
appears  single  in  some  parts,  in  others  double. 
Ltpd  364.  There  are  several  little  whitish  spots  in  the 

spots.  heavens,  which  appear  magnified,  and  more  lumi- 
nous when  seen  through  telescopes  ;  yet  without  any 
stars  in  them.  One  of  these  is  in  Andromeda's  gir- 
dle, and  was  first  observed  A.  D.  1612,  by  Simon 
Marius  :  it  has  some  whitish  rays  near  its  middle, 
is  liable  to  several  changes,  and  is  sometimes  invisi- 
ble. Another  is  near  the  ecliptic,  between  the  head 
and  bow  of  Sagittarius  :  it  is  small,  but  very  lu- 
minous. A  third  is  on  the  back  of  the  Centaur* 
which  is  too  far  south  to  be  seen  in  Britain.  A 
fourth,  of  a  smaller  size,  is  before  Antinous's  right 
foot,  having  a  star  in  it  which  makes  it  appear  more 
bright.  A  fifth  is  in  the  constellation  of  Hercules, 
between  the  stars  £  and  *,  which  spot,  though  but 
small,  is  visible  to  the  bare  eye,  if  the  sky  be  clear, 
and  the  Moon  absent. 

Cloudy  365.  Cloudy  stars  are  so  called  from  their  misty 
stars.  appearance.  They  look  like  dim  stars  to  the  naked 
eye  ;  but  through  a  telescope  they  appear  broad  illu- 
minated parts  of  the  sky  ;  in  some  of  which  is  one 
star,  in  others  more.  Five  of  these  are  mentioned 
by  Ptolemy.  \ .  One  at  the  extremity  of  the  right 
hand  of  Perseus.  2.  One  in  the  middle  of  the 
Crab.  3.  One,  unformed,  near  the  sting  of  the 
Scorpion.  4.  The  eye  of  Sagittarius.  5.  One  in 
the  head  of  Orion.  In  the  first  of  these  appear  more 
stars  through  the  telescope  than  in  any  of  the  rest, 
although  21  have  been  counted  in  the  head  of  Orion9 
:  and  above  forty  in  that  of  the  Crab.  Two  are  visi- 
ble in  the  eye  of  Sagittarius  without  a  telescope, 
and  several  more  with  it.  Flams  tead  observed  a 
cloudy  star  in  the  bow  of  Sagittarius,  containing 
many  small  stars  :  and  the  star  d  above  Sagittarius' s 
right  shoulder  is  encompassed  with  several  more. 
Both  Cassini  and  Flamstead  discovered  one  between 
the  Great  and  Little  Dog,  which  is  yery  full  of  stars. 


Of  new  Periodical  Stars. 

visible  only  by  the  telescope.  The  two  whitish  spots 
near  the  south  pole,  called  the  Magellanic  clouds  by 
sailors,  which  to  the  bare  eye  resemble  part  of  the 
Milky  Way,  appear  through  telescopes  to  be  amix-ni^c 
ture  of  small  clouds  and  stars.  But  the  most  re-  clouds, 
markable  of  all  the  cloudy  stars  is  that  in  the  middle 
of  Orion's  sword,  where  seven  stars  (of^which  three 
are  very  close  together)  seem  to  shine  through  a 
cloud,  very  lucid  near  the  middle,  but  faint  and  ill- 
defined  about  the  edges.  It  looks  like  a  gap  in  the 
sky,  through  which  one  may  see  (as  it  were)  part  of 
a  much  brighter  region.  Although  most  of  these 
spaces  are  but  a  few  minutes  of  a  degree  in  breadth, 
yet,  since  they  are  among  the  fixed  stars,  they  must 
be  spaces  larger  than  what  is  occupied  by  our  solar 
system  ;  and  in  which  there  seems  to  be  a  perpetual 
uninterrupted  day, among  numberless  worlds,which 
no  human  art  ever  can  discover. 

366.  Several  stars  are  mentioned  by  ancient  astro-  Changes 
nomers,  which  are  not  now  to  be  found  ;  and  others  J^ 
are  now  visible  to  the  bare  eye,  which  are  not  re- 
corded in  the  ancient  catalogue.     Hipparchus  ob- 
served a  new  star  about  120  years  before  CHRIST  ; 
but  he  has  not  mentioned  in  what  part  of  the  hea- 
vens it  was  seen,  although  it  occasioned  his  making 
a  catalogue  of  the  stars ;  which  is  the  most  ancient 
that  we  have. 

The  first  new. star  that  we  have  any  good  account  New 
of,  was  discovered  by  Cornelius  Gemma  on  the  8th 
of  Nove?/iber,  A.  D.  1572,  in  the  chair  of  Cassio- 
pea.  It  surpassed  Sirius  in  brightness  and  magni- 
tude ;  and  was  seen  for  16  months  successively.  At 
first  it  appeared  bigger  than  Jupiter,  to  some  eyes, 
by  which  it  was  seen  at  mid-day  ;  afterwards  it  de- 
cayed gradually  both  in  magnitude  and  lustre,  until 
March  1573,  when  it  became  invisible. 

On  the  13th  of  August  1596,  David  Fabricius 
observed  the  Stella  Mira,  or  wonderful  star,  in  the 
neck  of  the  Whale  ;  which  has  been  since  found  to 
appear  and  disappear  periodically  seven  times  in  six 


336  Of  new  Periodical  S'ars. 

years,  continuing  in  the  greatest  lustre  for  15  days 
together  ;  and  is  never  quite  extinguished. 

In  the  year  160O,  William  Janserims  discovered  a 
changeable  star  in  the  neck  of  the  Swan  ;  which,  in 
time,  became  so  small  as  to  be  thought  to  disappear 
entirely,  till  the  years  1657,  1658,  and  1 659,  when 
it  recovered  its  former  lustre  and  magnitude,  but 
soon  decayed ;  and  is  now  of  the  smallest  size. 

In  the  year  1 604,  Kepler  and  many  of  his  friends 
saw  a  new  star  near  the  heel  of  the  right  foot  of  Ser- 
pentarius,  so  bright  and  sparkling,  that  it  exceeded 
any  thing  they  had  ever  seen  before ;  and  took  notice 
that  it  was  every  moment  changing  into  some  of  the 
colours  of  the  rainbow,  except  when  it  was  near  the 
horizon,  at  which  time  it  was  generally  white.  It 
surpassed  Jupiter  in  magnitude,  which  was  near  it 
all  the  month  of  October  ^  but  easily  distinguished  from 
Jupiterby  the  steady  light  of  that  planet.  It  disap- 
peared between  October  16O5,  and  the  February  fol- 
lowing, and  has  not  been  seen  since  that  time. 

In  the  year  167O,  July  15,  Hevelius  discovered  a 
new  star,  which  in  October  was  so  decayed  as  to  be 
scarce  perceptible.  In  April  following  it  regained  its 
lustre,  but  wholly  disappeared  in  August.  In  March 
1672,  it  was  seen  again,  but  very  small ;  and  has  not 
since  been  visible. 

In  the  year  lt>86,  a  new  star  was  discovered  by 
Kirch,  which  returns  periodically  in  404  days. 

In  the  year  1672,  Cassini  saw  a  star  in  the  neck 
of  the  B nil,  which  he  thought  was  not  visible  in  Ty- 
cbo's  time ;  nor  when  Bayer  made  his  figures. 
Cannot  be  367.  Many  stars,  beside  those  above-mentioned, 
comets.  have  keen  observed  to  change  their  magnitudes ;  and 
as  none  of  them  could  ever  be  perceived  to  have  tails, 
it  is  plain  they  could  not  be  comets ;  especially  as 
they  had  no  parallax,  even  when  largest  and  bright- 
est. It  would  seem  that  the  periodical  stars  have  vast 
clusters  of  dark  spots,  and  very  slow  rotations  on 
their  axes  j  by  which  means,  they  must  disappear 


Of  Changes  In  the  Heavens.  337 

when  the  side  covered  with  spots  is  turned  towards  " 
us.  And  as  for  those  which  break  out  all  of  a  sud- 
den with  such  lustre,  it  is  by  no  means  improbable 
that  they  are  Suns  whose  fuel  is  almost  spent,  and 
again  supplied  by  some  of  their  comets  falling  upon 
them,  and  occasioningan  uncommonblaze  and  splen- 
dour for  some  time  :  which  indeed  appears  to  be  the 
greatest  use  of  the  cometary  part  of  any  system*. 

Some  of  the  stars,  particularly  ^rr/^rz/j,havebeen  Some  star* 
observed  to  change  their  places  above  a  minute  of  a thei 
degree  with  respect  to  others.    But  whether  this  beces- 
owing  to  any  real  morion  in  the  stars  themselves,  must 
require  the  observations  of  many  ages  to  determine. 
If  our  solar  system  change  its  place  with  regard  to 
absolute  space,  this  must  in  process  of  time  occasion 
an  apparent  change  in  the  distances  of  the  stars  from 
each  other :  and  in  such  a  case,  the  places  of  the  near- 
est stars  to  us  being  more  affected  than  those  which 
are  very  remote,  their  relative  positions  must  seem 
to  alter,  though  the  stars  themselves  were  really  im- 
moveable.    On  the  other  hand,  if  our  own  system 
be  at  rest,  and  any  of  the  stars  in  real  motion,  this 
must  vary  their  positions;  and  the  more  so,  the  nearer 
they  are  to  us,  or  the  swifter  their  motions  are;  or  the 

*  M.  Maupertius,  in  his  Dissertation  on  the  figures  of  the 
Celestial  Bodies  (p.  91 — 93),  is  of  opinion  that  some  stars,  by 
their  prodigious  quick  rotations  on  their  axes,  may  not  only 
assume  the  figures  of  oblate  spheroids,  but  that  by  the  great 
centrifugal  force  arising  from  such  rotations,  they  may  be- 
come ot  the  figures  of  mill-stones  ;  or  be  reduced  to  fiat  cir- 
cular planes,  so  thin  as  to  be  quite  invisible  when  their  edges 
are  turned  toward  us  ;  as  Saturn's  ring  is  in  such  positions. 
But  when  any  eccentric  planets  or  comets  go  round  any  flat 
star,  in  orbits  much  inclined  to  its  equator,  the  attraction 
of  the  planets  or  comets  in  their  perihelions  must  alter  the 
inclination  of  the  axis  of  that  star  ;  on  which  account  it  will 
appear  more  or  less  large  and  luminous,  as  its  broad  side  is 
more  or  less  turned  toward  us.  And  thus  he  imagines  we 
may  account  for  the  apparent  changes  of  magnitude  and  lus- 
tre in  those  stars,  and  likewise  for  their  appearing  and  dis- 
appearing. 


383  Of  Changes  in  the  Heavens. 

more  proper  the  direction  of  their  motion  is  for  our 
perception. 
The  eclip-      353.  rf  [le  obliquity  of  the  ecliptic  to  the  equinoc- 

tic  lessob-    .    .  .     r  J         ,         .  11-  r 

lique  now  tial  is  round  at  present  to  be  above  the  third  part  or  a 
to  the  degree  less  than  Ptolemy  found  it.  Arid  most  of  the 
thaiTfor-  observers  after  him  found  it  do  decrease  gradually 
down  to  Tycho's  time.  If  it  be  objected,  that  we 
cannot  depend  on  the  observations  of  the  ancients, 
because  of  the  incorrectness  of  their  instruments;  we 
have  to  answer,  that  both  Tycho  and  llamstead  arc 
allowed  to  have  been  very  good  observers  ;  and  yet 
we  find  that  Flamstead  makes  this  obliquity  24  mi- 
nutes of  a  degree  less  than  Tycho  did,  about  10O 
years  before  him  :  and  as  Ptolemy  was  ]  324  years  be- 
fore  Tycho,  so  the  gradual  decrease  answers  nearly 
to  the  difference  of  time  between  these  three  astrono- 
mers. If  we  consider,  that  the  Earth  is  not  a  per- 
fect sphere,  but  an  oblate  spheroid,  having  its  axis 
shorter  than  its  equatorial  diameter;  and  thatthe  Sun 
and  Moon  are  constantly  acting  obliquely  upon  the 
greater  quantity  of  matter  about  the  equator,- pulling 
it  as  it  were  toward  a  nearer  and  nearer  coincidence 
with  the  ecliptic  ;  it  will  not  appear  improbable  that 
these  actions  should  gradually  diminish  the  angle  be- 
tween those  planes.  Nor  is  it  less  probable  that  the 
mutual  attraction  of  all  the  planets  should  have  a  ten- 
dency to  bring  their  orbits  to  a  coincidence ;  but  this 
change  is  too  small  to  become  sensible  in  many 
ages.* 

*  M.  de  la  Grange  has  demonstrated,  in  the  most  satisfac- 
tory manner,  that  no  permanent  change  can  take  place  in  the 
magnitudes,  figures,  or  inclinations,  of  the  planetary  orbits  ; 
and  that  the  periodical  changes  are  confined  within  very 
narrow  limits :  the  ecliptic  therefore,  will  never  coincide 
with  the  equator,  nor  change  its  inclination  above  2  degrees. 
In  short,  the  solar  planetary  system  oscillates,  as  it  were, 
round  a  medium  state,  from  which  it  never  swerves  very 
far.  See  note  subjoined  to*p.  1 16. 


Of  the  Division  of  Time.  3SO 


CHAP.  XXL 

Of  the  Division  of  Time.    A  perpetual  Table  of  Nev, 
Moons.     The  Times  of  the  Birth  and  Death  of 
CHRIST.    A  Table  of  remarkable  JEras  or  Events. 


369  TPHE  parts  of  time  are,   seconds,  minutes, 
JL    hours  9  days,  years,  cycles,  ages,  and  pe- 
riods. 

370.  The  original  standard,  or  integral  measure  A  year. 
of  time,  is  a  year  ;   which  is  determined  by  the  re- 
volution of  some  celestial  body  in  its  orbit,  viz.  the 

Sun  or  Moon. 

371.  The  time  measured  by  the  Sun's  revolution  Tro^c* 
in  the  ecliptic,  from  any  equinox  or  solstice  to  the>e 
same  again,    is  called  the  solar  or  tropical  year, 
which  contains  365  days,  5  hours,  48  minutes,  57 
seconds  ;  and  is  the  only  proper  or  natural  year,  be- 
cause it  always  keeps  the  same  seasons  to  the  same 
"months. 

372.  The  quantity  of  time  measured  by  the  Sun's  siderea 
revolution  as  from  any  fixed  star  to  the  same  starycar- 
again,  is  called  the  sidereal  year  ;   which  contains 

365  days,  6  hours,  9  minutes,  14}  seconds,  and  is 
20  minutes  171  seconds  longer  than  the  true  solar 
year. 

373.  The  time  measured  by  twelve  revolutions  of  Lunar 
the  Moon,  from  the  Sun  to  the  Sun  again,  is  called  ye 
the  lunar  year  ;  it  contains  354?  days,  8  hours,  48 
minutes,  36  seconds  ;  and  is  therefore  1O  days,  21 
hours,  O  minutes,  21  seconds  shorter  than  the  solar 
year.     This  is  the  foundation  of  the  epact. 

374.  The  civil  year  is  that  which  is  in  common  civil 
use  among  the  different  nations  of  the  world  ;  of  yea!% 
which,  some  reckon  by  the  lunar,  but  most  by  the 
solar.     The  civil  solar  year  contains  365  days,  £02* 
three  years  running,  which  are  called  common  years  ; 
and  then  comes  in  what  is  called  the  bissextile  or 


«-:  90  Of  the  Division  of  Time. 

leap-year,  which  contains  366  days.  This  is  also 
called  the  Julian  year*  on  account  of  Julius  C&sar, 
who  appointed  the  intercalary  day  every  fourth  year, 
thinking  thereby  to  make  the  civil  and  solar  year 
keep  pace  together.  And  this  day,  being  added  to 
the  23d  of  February,  which  in  the  Roman  calendar 
was  the  sixth  of  the  Calends  of  March,  that  sixth  day 
was  twice  reckoned,  or  the  23d  and  24th  were  reck- 
oned as  one  day  ;  and  was  called  Bis  sextus  dies,  and 
thence  came  the  name  bissextile  for  that  year.  But 
in  our  common  almanacks  this  day  is  added  at  the 
end  of  February. 

year"  ^ 5'  ^ne  civil  lunar  year  is  also  common  or  in- 

tercalary. The  common  year.consists  of  12  luna- 
tions, which  contain  354  days ;  at  the  end  of  which 
the  year  begins  again.  The  intercalary,  or  embo- 
limic  year,  is  that  wherein  a  month  was  added  to 
adjust  the  lunar  year  to  the  solar.  This  method  was 
used  by  the  Jews,  who  kept  their  account  by  the 
lunar  motions.  But  by  intercalating  no  more  than  a 
month  of  30  days,  which  they  called  Ve-Adar,  every 
third  year,  they  fell  3|  days  short  of  the  solar  year  in 
that  time. 

Roman  376.  The  Romans  also  used  the  lunar  embolimic 
year  at  first,  as  it  was  settled  by  Romulus  their  first 
king,  who  made  it  to  consist  only  of  ten  months  or 
lunations ;  which  fell  6 1  days  short  of  the  solar  year, 
and  so  their  year  became  quite  vague  and  unfixed ; 
for  which  reason  they  were  forced  to  have  a  table 
published  by  the  high-priests,  to  inform  them  when 
the  spring  and  other  seasons  began.  But  Julius  Cte- 
sar,  as  already  mentioned,  §  374,  taking  this  trou- 
'  bleso  me  affair  into  consideration,  reformed  the  calen- 
dar, by  making  the  year  to  consist  of  365  days  6 
hours. 

The  origi.      377.  The  year  thus  settled,  is  what  was  used  in 

^rellrfal  Britain  till  A.  D.  1752  :  but  as  it  is  somewhat  more 

or  new      than  1 1  minutes  longer  than  the  solar  tropical  year, 

the  times  of  the  equinoxes  go  backward,  and  fall 

earlier  by  one  day  in  about  130  years.    In  the  time 


Of  the  Division  of  Time.  391 

of  the  Nicene  council  ( A.  D.  325),  which  was  1439 
years  ago,  the  vernal  equinox  fell  on  the  21st  of 
"March:  and  if  we  divide  1444  by  130,  it  will  quote 
11,  which  is  the  number  of -days  the  equinox  has 
fallen  back  since  the  council  of  Nice.  This  causing 
great  disturbances,  by  unfixing  the  times  of  the  cele- 
bration of  Easter,  and  consequently  of  all  the  other 
moveable  feasts,  pope  Gregory  the  XIII,  in  the  year 
1582,  ordered  ten  clays  to  be  at  once  stricken  out  of 
that  year;  and  the  next  day  after  the  fourth  of  Octo- 
ber was  called  the  fifteenth.  By  this  means,  the  ver- 
nal equinox  was  restored  to  the  21st  of  March;  and 
it  was  endeavoured,  by  the.  omission  of  three  inter- 
calary days  in  400  years,  to  make  the  civil  or  politi- 
cal year  keep  pace  with  the  solar  for  the  time  to  come. 
This  new  form  of  the  year  is  called  the  Gregorian 
account,  or  new  style  ;  which  is  received  in  all  coun- 
tries where  the  pope's  authority  is  acknowledged,  and 
ought  to  be  in  all  places  where  truth  is  regarded. 

378.  The  principal  division  of  the  year  is  into  Month* 
months,  which  are  of  two  sorts,  namely,  astronomi- 
cal and  civil.  The  astronomical  month  is  the  time 
in  which  the  Moon  runs  through  the  zodiac,  and  is 
either  periodical  or  si/nodical.  The  periodical  month 
is  the  time  spent  by  the  Moon  in  making  one  com- 
plete revolution  from  any  point  of  the  zodiac  to  the 
same  again ;  which  is  27d  7U  43m.  The  synodical 
month,  called  a  lunation,  is  the  time  contained  be- 
tween the  Moon's  parting  with  the  Sun  at  a  conjunc- 
tion, and  returning  to  him  again ;  which  is  29d  121* 
44m.  The  civil  months  are  those  which  are  framed 
for  the  uses  of  civil  life ;  and  are  different  as  to  their 
names,  number  of  days,  and  times  of  beginning,  in 
several  different  countries.  The  first  month  of  the 
Jewish  Year  fell,  according  to  the  Moon,  in  our  Au- 
gust and  September,  old  style ;  the  second  in  Sep- 
tember and  October;  and  so  on.  The  first  month 
of  the  Egyptian  year  began  on  the  29th  of  our  Au- 
gust. The  first  month-  of  the  Arabic  and  Turkish 

3D 


392  Of  the  Division  of  Time. 

I/ear  began  the  16th  ofJttly.  The  first  month  of 
the  Grecian  year  fell,  according  to  the  Moon,  in 
June  and  July,  the  second  in  July  and  August,  and 
so  on,  as  in  the  following  table. 

379.  A  month  is  divided  into  four  parts  called 
-weeks,  and  a  week  into  seven  parts  called  days  ;  so 
that  in  a  Julian  year  there  are  13  such  months,  or  52 
weeks,  and  one  day  over.  The  Gentiles  gave  the 
names  of  the  Sun,  Moon,  and  planets,  to  the  days 
of  the  week.  To  the  first,  the  name  of  the  Sun ; 
to  the  second,  of  the  Moon  ;  to  the  third,  of  Mars  ; 
to  the  fourth,  of  Mercury  ;  to  the  fifth,  of  Jupiter  ; 
to  the  sixth,  of  Venus;  and  to  the  seventh,  of  Sa- 
turn. 


ST°                  The  Jewish 

year. 

Days'S 
c 

1  Tisri 

Aug.  —  Sept. 

30 

2  Marchesvan    

Sept.—  Oct. 

29    s 

3  Casleau           

Oct.  —  Nov. 

30    ^ 

4  Tebeth 

Nov  —  Dec. 

29    ^ 

5  Shebat 

Dec.  —  Jan. 

30    S 

6  Adar 

Jan.  —  Feb. 

29    ? 

7NisanorAbib      — 

Feb  —  Mar. 

30    s 

SJiar 

Mar.  —  Apr. 

29    ^ 

9Sivan 

Apr.—  May 

30    ^ 

10  Tamuz 

May  —  June 

29    \ 

11  Ab 

June  —  July 

30    > 

12  Elul 

July  —  Aug. 

29    \ 

s 

Days  in  the  year  — 

354    <; 

S  In  the  embolimic  year  after  Adar  they  added  a  Ij 
!j  month  called  Fe-Adar,  of  30  days.  £ 

Vflt  ^S^ 


Of  the  Division  of  Time. 


393 


>N° 

The  Egyptian  year. 

Days  J; 

s 

* 

Thoth         August 

29 

30    s 

S     2 

Paophi        September 

28 

30    \ 

SS     3 

Athir          October 

28 

30  ; 

«!     4 

Chojac       November 

27 

30    £ 

>     5 

Tybi          December 

27 

30    S 

5     6 

Mechir       January 

26 

30    S 

S     7 

Phamenoth  February 

25 

30    s 

8 

Parmuthi  March 

27 

30    ^ 

SS     9 

Pachon      April 

26 

30    £ 

5  10 

Payni         May 

26 

30    V 

Epiphi       June 

25 

30    ? 

\  12 

Mesori       July 

25 

30    S 

S        Epagomenx  or  days  added 

^ 

<J        Days  in  the  year. 

\/\/\ 

365    £ 

/\x",y,X^j 

5^^%^*sX\j 

The  Arabic  and  Turkish  year. 

~*r^- 

s-*r*r*r$ 

Days'5; 

s 

c 

\     1 

Muharram  —  —  July 

16 

30    S 

2 

Saphar        August 

15 

29    s 

3 

Rabia  I.      September 

13 

30    ^ 

S     4 

Rabia  II.    October 

13 

29    ^ 

S      5 

Jornada  I.  November 

11 

30    \ 

s    6 

Jornada  II.  December 

11 

29    S 

s    7 

Rajab         January 

9 

30    S 

S     8 

Shasban     February 

8 

29    s 

s     9 

Ramadam  March 

9 

30    \ 

Shawal       —  —  April 

8 

29    £ 

s  n 

Dulhaadah  —  —  May 

7 

30    \ 

\  12 

Dulheggia  —  —  June 

5 

29    ^ 

S          Days  in  the  year 

354    ^ 

S  The  Arabians  add  1 1  days  at  the  end  of  every  s 
s  year,  which  keep  the  same  months  to  the  same  s 
\  seasons.  > 


Of  the  Division  of  Time. 


s 

The  ancient 

Grecian  year. 

Day  3*1 

S      1 

Hecatombaeon  — 

—  June  —  July 

30    S 

s    2 

Metagitnion      — 

—  July  —  Aug. 

29    S 

S     3 

Boedromion     — 

—  Aug.  —  Sept. 

30    s 

I     4 

Pyanepsion       — 

_  Sept.—  Oct. 

29    \ 

SS     5 

Maimacterion  — 

—  Oct.  —  Nov. 

30    > 

5   6 

Posideon 

—  Nov.  —  Dec. 

29    £ 

S   7 

Gamelion 

—  Dec.  —  Jan. 

30 

S     8 

Anthesterion    — 

—  Jan.  —  Feb. 

29    s 

SS     9 

Elaphebolion   — 

—  Feb.  —  Mar. 

30    5 

s  10 

Municheon      — 

—  Mar.  —  Apr. 

29    !; 

^ 

Thargelion       — 
Schirrophorion 

—  -  Apr.  —  May 
—  May  —  June 

30    £ 
29    S 

Ij          Days  in  the  year 

— 

354    £ 

Days.  380.  A  day  is  either  natural  or  artificial.  The 

natural  day  contains  24  hours;  the  artificial,  the 
time  from  Sun-rise  to  Sun-set.  The  natural  day  is 
either  astronomical  or  civil.  The  astronomical  day 
begins  at  noon,  because  the  increase  and  decrease 
of  days  terminated  by  the  horizon  are  very  unequal 
among  themselves;  which  inequality  is  likewise 
augmented  by  the  inconstancy  of  the  horizontal  re- 
fractions, ^  183;  and  therefore  the  astronomer  takes 
the  meridian  for  the  limit  of  diurnal  revolutions ; 
reckoning  noon,  that  is,  the  instant  when  the  Sun's 
centre  is  on  the  meridian,  for  the  beginning  of  the 
day.  The  Uritish,  French,  Dutch,  Germans,  Span- 
iards, Portuguese,  and  Egyptians,  begin  the  civil 
day  at  midnight :  the  ancient  Greeks,  Jews,  Bohe- 
mians, Silesians,  with  the  modern  Italians  and  Chi- 
nese, begin  it  at  Sun- setting :  and  the  ancient  Baby- 
lonians, Persians,  Syrians,  with  the  modern  Greeks, 
at  Sun-rising. 

Hour».  381.  An  hour  is  a  certain  determinate  part  of  the 
day,  and  is  either  equal  or  unequal.  An  equal  hour 
is  the  24th  part  of  a  mean  natural  day,  as  shewn  by 


Of  the  Division  of  Time.  395 

well-regulated  clocks  or  watches  ;  but  these  hours 
are  not  quite  equal  as  measured  by  the  returns  of 
the  Sun  to  the  meridian,  because  of  the  obliquity  of 
the  ecliptic,  and  Sun's  unequal  motion  in  it,  \  224 
— 245.  Unequal  hours  are  those  by  which  the  arti- 
ficial day  is  divided  into  twelve  parts,  and  the  night 
into  as  many. 

382.  An  hour  is  divided  into  60  equal  parts  called  Minutes, 
mnutes,  a  minute  into  60  equal  parts  called  seconds,  scponds> 

„     .      /  •     T     thirds, and 

and  these  again  into  60  equal  parts  called  thirds.  SCrupies. 
The  Jews,  Chaldeans,  and  Arabians,  divide  the  hour 
into  1080  equal  parts  called  scruples;  which  num- 
ber contains  18  times  60,  so  that  one  minute  con- 
tains 18  scruples. 

383.  A  cycle  is  a  perpetual  round,  or  circulation  cycles  of 
of  the  same  parts  of  time  of  any  sort.    The  cycle  qf^G  Sun» 
the  Sun  is  a  revolution  of  28  years,  in  which  time  iS"t*ion. 
the  days  of  the  month  return  again  to  the  same  days 

of  the  week ;  the  Sun's  place  to  the  same  signs  and 
degrees  of  the  ecliptic  on  the  same  months  and  days, 
so  as  not  to  differ  one  degree  in  100  years ;  and  the  . 
leap-years  begin  the  same  course  over  again  with 
respect  to  the  days  of  the  week  on  which  the  days 
of  the  months  fall.  The  cycle  of  the  Moon,  com- 
monly called  the  golden  number,  is  a  revolution  of 
19  years;  in  which  time,  the  conjunctions,  oppo- 
sitions, and  other  aspects  of  the  Moon,  are  within 
an  hour  and  half  of  being  the  same  as  they  were  on 
the  same  days  of  the  months  19  years  before.  The 
Indiction  is  a  revolution  of  15  years,  used  only  by 
the  Romans  for  indicating  the  times  of  certain  pay- 
ments made  by  the  subjects  to  the  republic :  it  was 
established  by  Constantine,  A.  D.  312. 

384.  The  year  of  our  SAVIOUR'S  birth,  according  TO  find 
to  the  vulgar  sera,  was  the  9th  year  of  the  solar  cycle ; the  years 
the  first  year  of  the  lunar  cycle ;  and  the  312th  year 

after  his  birth  was  the  first  year  of  the  Roman  indic- 
tion.  Therefore  to  find  the  year  of  the  solar  cycle, 
add  9  to  any  given  year  of  CHRIST,  and  divide  the 
sum  by  28,  the  quotient  is  the  number  of  cycles 


.396  Of  the  Division  of  Time. 

elapsed  since  his  birth,  and  the  remainder  is  the  cycle 
for  the  given  year:  if  nothing  remain,  the  cycle  is  28. 
To  find  the  lunar  cycle,  add  I  to  the  given  year  of 
CHRIST,  and  divide  the  sum  by  19  ;  the  quotient  is 
the  number  of  cycles  elapsed  in  the  interval,  and  the 
remainder  is  the  cycle  for  the  given  year  :  if  nothing- 
remain,  the  cycle  is  19.  Lastly,  subtract  312  from 
the  given  year  of  CHRIST,  and  divide  the  remainder 
by  15  ;  and  what  remains  after  this  division  is  the 
indictlon  for  the  given  year:  if  nothing  remain,  the 
indiction  is  15. 

Thedefi-  385.  Although  the  above  deficiency  in  the  lunar 
th^iunar  cjc^e  °f  an  ^our  anc^  half  every  19  years  be  but 
cycle,  and  smallj  yet  in  time  it  becomes  so  sensible  as  to  make 
a  w^e  "atural  day  m  3K)  years.  So  that,  although 
this  cycle  be  of  use,  when  the  golden  numbers  are 
rightly  placed  against  the  days  of  the  months  in  the 
calendar,  as  in  our  Common  Prayer  Books,  for  find- 
ing the  days  of  the  mean  conjunctions  or  oppositions 
of  the  Sun  and  Moon,  and  consequently  the  time  of 
Raster ;  it  will  only  serve  for  310  years,  old  style. 
For  as  the  new  and  full  Moons  anticipate  a  day  in 
that  time,  the  golden  numbers  ought  to  be  placed 
one  day  earlier  in  the  calendar  for  the  next  310 
years  to  come.  These  numbers  were  rightly  placed 
against  the  days  of  new  Moon  in  the  calendar, 
by  the  council  of  Nice,  A.  D.  325  ;  but  the  antici- 
pation, which  has  been  neglected  ever  since,  is  now 
grown  almost  into  5  days;  and  therefore  all  the  golden 
numbers  ought  now  to  be  placed  5  days  higher  in 
the  calendar  for  the  old  style  than  they  were  at  the 
time  of  the  said  council ;  or  six  days  lower  for  the 
new  style  ^  because  at  present  it  differs  1 1  days  from 
the  old. 

to         386.  In  the  annexed  table,  the  golden  numbers 
*|nd  the     uncjer  the  months  stand  I'.irainst  the  days  of  new 

day  of  the  ..  r  •       *      i    r    i  i  ^  r         >  / 

new  Moon  Moon  in  tlie  left-hand  column,  lor  the  new  style  ; 

by  the       adapted  chiefly  to  the  second  year  after  leap-year,  as 

number,     being  the  nearest  mean  for  all  the  four ;  and  will  serve 

till  the  year  1900.  Therefore,  to  find  the  day  of  new 


Of  the  Division  of  Time. 


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398  Of  the  Division  of  Time. 

Moon  in  any  month  of  a  given  year  till  that  time, 
look  for  the  golden  number  of  that  year  under  the 
desired  month,  and  against  it,  you  have  the  clay  of 
new  Moon,  in  the  left-hand  column.  Thus,  suppose 
it  were  required  to  find  the  day  of  new  Moon  in 
September  1757;  the  golden  number  for  that  year 
is  10,  which  I  look  for  under  September,  and  right 
against  it  in  the  left-hand  column  I  find  13,  which 
is  the  day  of  new  Moon  in  that  month.  A".  B.  If 
all  the  golden  numbers,  except  17  and  6,  were  set 
one  day  lower  in  the  table,  it  would  serve  from  the 
beginning  of  the  year  1900  till  the  end  of  the  year 
2199.  The  first  table  after  this  chapter  shews  the 
golden  number  for  4000  years  after  the  birth  of 
CHRIST  ;  by  looking  for  the  even  hundreds  of  any 
given  year  at  the  left  hand,  and  for  the  rest  to  make 
up  that  year  at  the  head  of  the  table ;  and  where  the 
columns  meet,  you  have  the  golden  number  (which 
is  the  same  both  in  old  and  new  style}  for  the  given 
year.  Thus,  suppose  the  golden  number  was  want- 
ed for  the  year  1757;  I  look  for  1700  at  the  left 
hand  of  the  table,  and  for  57  at  the  top  of  it;  then 
guiding  my  eye  downward  from  57  to  over  against 
1700,  I  find  10,  which  is  the  golden  number  for 
that  year. 

A  perpe-  387.  But  because  the  lunar  cycle  of  19  years  some- 
ofatheble  times  includes  five  leap-years, and  at  other  times  only 
time  of  four,  this  table  will  sometimes  vary  a  day  from  the 
to  the*0™ trut^  *n  leap-years  after  February.  And  it  is  impos- 
nearest  sible  to  have  one  more  correct,  unless  we  extend  it 
hour  for  to  four  times  19  or  76  years ;  in  which  there  are  19 
leap-years  without  a  remainder.  But  even  then  to 
have  it  of  perpetual  use,  it  must  be  adapted  to  the 
old  style ;  because  in  every  centurial  year  not  divi- 
sible by  4,  the  regular  course  of  leap-years  is  inter- 
rupted in  the  new ;  as  will  be  the  case  in  the  year 
1800.  Therefore,  upon  the  regular  old  style  plan,  I 
have  computed  the  following  table  of  the  mean  times 
of  all  the  new  Moons  to  the  nearest  hour  for  76  years; 


Of  the  Division  of  Time.  399 

beginning  with  the  year  of  CHRIST  1724,  and  end- 
ing with  the  year  1800. 

This  table  may  be  made  perpetual,  by  deducting 
6  hours  from  the  time  of  new  Moon  in  any  given 
year  and  month  from  1724  to  1800,  in  order  to  have 
the  mean  time  of  new  Moon  in  any  year  and  month 
76  years  afterward;  or  deducting  12 hours  for  152 
years,  18  hours  for  228  years,  and  24  hours  for 
304  years :  because  in  that  time  the  changes  of  the 
Moon  anticipate  almost  a  complete  natural  day.  And 
if  the  like  number  of  hours  be  added  for  so  many 
years  past,  we  shall  have  the  mean  time  of  any  new 
Moon  already  elapsed.  Suppose,  for  example,  the 
mean  time  of  change  was  required  for  January, 
1802;  deduct  76  years,  and  there  remains  1726, 
against  which,  in  the  following  table,  under  January, 
I  find  the  time  of  new  Moon  was  on  the  21st  day, 
at  1 1  in  the  evening ;  from  which  take  6  hours,  and 
there  remains  the  21st  day,  at  5  in  the  evening,  for 
the  mean  time  of  change  in  January  1802.  Or,  if 
the  time  be  required  for  May,  A.  D.  1701,  add  76 
years,  and  it  makes  1777,  which  I  look  for  in  the 
table,  and  against  it,  under  May,  I  find  the  new 
Moon  in  that  year  falls  on  the  25th  day,  at  9  in  the 
evening ;  to  which  add  6  hours,  and  it  gives  the  26th 
day,  at  3  in  the  morning,  for  the  time  of  new  Moon 
in  May,  A.  D,  1701.  By  this  addition  for  time 
past,  or  subtraction  for  time  to  come,  the  table  will 
not  vary  24  hours  from  the  truth  in  less  than  14592 
years.  *  And  if,  instead  of  6  hours  for  every  76 
years,  we  add  or  subtract  only  5  hours  52  minutes, 
it  will  not  vary  a  day  in  10  millions  of  years. 

Although  this  table  is  calculated  for  76  years  only, 
and  according  to  the  old  style,  yet  by  means  of  two 
easy  equations  it  may  be  made  to  answer  as  exactly 
to  the  new  style,  for  any  time  to  come.  Thus,  be- 
cause the  year  1724  in  this  table  is  the  first  year  of 
the  cycle  for  which  it  is  made ;  if  from  any  year  of 

3E 


400  Of  the  Division  of  Time. 

CHRIST  after  1800  you  subtract  1723,  and  divide 
the  overplus  by  76,  the  quotient  will  shew  how 
*  many  entire  cycles  of  76  years  are  elapsed  since  the 
beginning  of  the  cycles  here  provided  for ;  and  the 
remainder  will  shew  the  year  of  the  current  cycle 
answering  to  the  given  year  of  CHRIST.  Hence,  if 
the  remainder  be  0,  you  must  instead  thereof  put 
76,  and  lessen  the  quotient  by  unity. 

Then,  look  in  the  left-hand  column  of  the  table 
for  the  number  in  your  remainder,  ^nd  against  it 
you  will  find  the  times  of  all  the  mean  new  Moons  in 
that  year  of  the  present  cycle.  And  whereas  in  76 
Julian  years  the  Moon  anticipates  5  hours  52  mi- 
nutes, if  therefore  these  5  hours  52  minutes  be 
multiplied  by  the  above-found  quotient,  that  is,  by 
the  number  of  entire  cycles  past ;  the  product  sub- 
tracted from  the  times  in  the  table  will  leave  the  cor- 
rected times  of  the  new  Moons  to  the  old  style ; 
\vhich  may  be  reduced  to  the  new  style  thus : 

Divide  the  number  of  entire  hundreds  in  the  given 
year  of  CHRIST  by  4,  multiply  this  quotient  by  3, 
to  the  product  add  the  remainder,  and  from  their 
sum  subtract  2 :  this  last  remainder  denotes  the 
number  of  days  to  be  added  to  the  times  above  cor- 
rected, in  order  to  reduce  them  to  the  new  style. 
The  reason  of  this  is,  that  every  400  years  of  the 
new  style  gains  3  days  upon  the  old  style :  one  of 
which  it  gains  in  each  of  the  centurial  years  succeed- 
ing that  which  is  exactly  divisible  by  4  without  a  re- 
mainder ;  but  then,  whon  you  have  found  the  days 
so  gained,  2  must  be  subtracted  from  their  number 
on  account  of  the  rectifications  made  in  the  calen- 
dar by  the  council  of  Nice,  and  since  by  pope  Gre* 
gory.  It  must  also  be  observed,  that  the  additional 
days  found  as  above-  directed  *  do  not  take  place  in 
the  centurial  years  which  are  not  multiples  of  4  till 
February  29th  old  style,  for  on  that  day  begins  the 
difference  between  the  styles;  till  which  day,  there- 


Of  the  Division  of  Time*  401 

fore,  those  that  were  added  in  the  preceding  years 
must  be  used.  The  following  example  will  make 
this  accommodation  plain* 

Required  the  mean  time  of  new  Moon  in  June,  A,  D» 
1909  A*.  S. 

From    1909  take   1723 

yearsj    and  there    re- 
mains   .  .  .  .  * 186 

Which  divided  by  76, 

gives   the  quotient  2 

and  the  remainder .  »  .  34 
Then  against  34  in  the 

table  is  June 5d  8h  Om  afternoon* 

And  5h  52m  multiplied  by 

2  make  to  be  subtn  *        11  44 
Remains  the  mean  time 

according    to  the  old 

style,  June  * 5d  8k  16* 

Entire  hundreds  in  1909 

are  19,   which  divide 

by  4,  quotes  ....*.  4 
And  leaves  a  remainder  of  3 
Which  quotient  multipli- 
ed by  3  makes  12,  and 

the  remainder    added 

makes 15 

From  which  subtract  2, 

and  there  remains ...  13 
Which  number  of  days 

added  to  the  above  time, 

old  style,  gives  June. .  18d  8*  16m  morn.  M  S. 

So  the  mean  time  of  new  Moon  in  June  1909, 
nev>  style,  is  the  18th  day,  at  16  minutes  past  8  in 
the  morning. 


402  Of  the  Division  of  Time. 

If  11  days  be  added  to  the  time  of  any  new 
Moon  in  this  table,  it  will  give  the  time  of  that  new 
Moon  according  to  the  new  style  till  the  year  1800. 
And  if  14  days  18  hours  22  minutes  be  added  to 
the  mean  time  of  new  Moon  in  either  style,  it  will 
give  the  mean  time  of  the  next  full  Moon  according 
to  that  style. 


Of  the  Division  of  Time. 


403 


s' 

•/TABLE  shewing  the  Times  of  all  the  mean  Changes  S 

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of  the  Moon,  to  the  nearest  Hour,  through  four  ^ 

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404 


Of  the  Division  of  Time. 


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s  £ 

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Of  the  Division  of  Time. 


405 


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406 


Of  the  Division  of  Time. 


S   £ 

A  TABLE  of  the  mean  New  Moons  continued.   S 

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407 


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408 


Of  the  JDwision  of  Time. 


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51 

S  *p 

A  TABLE  of  the  mean  New  Moons  continued.   S 

A.D. 

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1773 

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4      12  A 

3       1  A 

3       2M  t 

$51 

1774 

24       9M 

23      10  A 

22     11M 

21      HAS 

* 

1775 

13       6A 

13       7M 

11        8  A 

11       9M  s 

\a 

1776 

32       2M 

1        3  A 

1       4M 

29        5  A 

29        5M  ^ 

Of  the  Division  of  Time. 


409 


is 

58, 

ll 

^  TABLE  0/"fAe  mean  JVew  Moons  concluded.    S 

A.D. 

January 

February 

March 

April      <| 

D.        H. 

D.        H. 

D.        H 

D.        H.  !j 

S  54 

1777 

27        6  A 

26       7M 

27       8  A 

26        9M  S 

«J  55 

1778 

17       3M 

15        4A 

17        5M 

15        6  A  ^ 

S56 

1779 

6       OA 

5        1M 

6       2  A 

5        3M  t 

J57 

1780 

25      10M 

23      11  A 

24      11M 

22      12  AS 

$58 

1781 

13        6A 

12        7M 

13        8  A 

12        9M  > 

$ 

^ 

1782 

3       3M 

1        4A 

3        5M 

1       6  A? 

S60 

1783 

22        1M 

20       2  A 

22        2M 

20       3  A  S 

s 

$61 

1784 

11       9M 

9      10  A 

10     11M 

8     12  AS 

$62 

1785 

29       7M 

27        8  A 

29        9M 

27      10  AS 

S  63 

1786 

18       4A 

17        5M 

18        5  A 

17        6M  £ 

£  64 

1787 

7     12  A 

6       1  A 

8       2M 

6       3  A  s 

5  65 

1788 

26      10  A 

25      11M 

25      12  A 

24        1  A  5 

S  66 

1789 

15        7M 

13        8A 

15        9M 

13      10  A  ^ 

S67 

1790 

4        4  A 

3        5JV1 

4        5  A 

3       6M  S 

S  68 

1791 

23        1  A 

22        2M 

23        3  A 

22        4M  S 

5j  69 

1792 

12      10  A 

11     11M 

11      12  A 

10        1  A$ 

$70 

1793 

1        7M 

30       8  A 

1        9M 
30      10  A 

29      10M  S 

j*l 

;;794 

20        5M 

18       6A 

20        6M 

18       7A  jj 

$72 

1795 

9        1  A 

8       2M 

9        3  A 

8        4M  ^ 

S  73 

1796 

28      HM 

26     12  A 

27       0  A 

26        1M  |j 

S74 

1797 

16       7  A 

15        8M 

16        9  A 

15      10M  S 

S 

|»75 

1798 

6       4M 

4        5  A 

6        6M 

4       7AS 

^76 

1799 

25       2M 

23       3  A 

25        4M 

23       5  AS 

s  *j 

1800 

14     11M 

12      12  A 

13       0  A 

12       1M  \ 

The  year  1 800  begins  a  new  cycle, 


410 


Of  the  Division  of  Tune, 


if 

S     ^ 

S  54 

A  TABLE  of  the  mean  New  Moons  concluded.    S 

A.D 

May 

June 

July 

S 

August     £ 

D.        H. 

D.         H 

D.        H. 

D.        H.  S 

1777 

25        9  A 

24      10M 

23      1  1  A 

22  "     0  A  S 

S  55 

1778 

15        6M 

13       7A 

13        8M 

11        9  A^ 

S  56 

1779 

4        3  A 

3       4M 

2       5  A 

1        6MS 

30        6  A  !j 

S  57 

1780 

22        0  A 

21        1M 

20        2  A 

19        3  A  S 

i  58 

1781 

11        9  A 

10     10M 

9      11  A 

8       OM  J[ 

S  59 

1782 

1        6M 

30        7  A 

29        8M 

28        9  A 

27       9M  S 

i" 

1783 

20        3M 

18       4  A 

18       5M 

16        6  A  S 

1784 

8        0  A 

7       1M 

6        2  A 

5        SMJ; 

62 

1785 

27      10M 

25      11  A 

25        0  A 

24        1M  £ 

63 

1786 

16        6  A 

15        7M 

14       8  A 

13        9MS 

64 

1787 

6       3M 

4       4  A 

4       5M 

2     6  A!; 

65 

1788 

24        1M 

22        2  A 

22       3M 

20       4  AS 

66 

1789 

13      10M 

11      11  A 

11       OA 

10        IMS 

67 

1790 

2        6  A 

1       7M 
30        8  A 

30       9M 

S 

28        9  A  jj 

^  68 

1791 

21        4  A 

20       5M 

19        6  A 

18       7M5 

]>  69 

1792 

10        1M 

8       2  A 

8        3M 

6       4AS 

i>  70 

1793 

28      11  A 

27       0  A 

27        1M 

25        1  A  Jj 

<!  71 

1794 

18       7M 

16       8  A 

16       9M 

14      10  A  ^ 

^72 

1795 

7       4A 

6        5M 

5       6A 

4       7MS 

S  73 

1796 

25        1  A 

24       2M 

23       3  A 

22       4M  £ 

S74 

1797 

14      10  A 

13     11M 

12      12  A 

11        1  AS 

S  75 

1798 

4       7M 

2       8A 

2       9M 
31      10A 

30     IOM  S 

S  76 

1799 

23        5M 

21        6A 

21        6M 

19        8A> 

S     1 

1800 

11        1  A 

10       2M 

9       3  A 

8       4Mt 

Of  the  Division  of  Time. 


411 


f  3 

A  TABLE  of  the  mean  New  Moons  concluded.      S 

S   ? 

s  £•> 

Se  fit  ember 

October 

November 

Dec.        $ 

j| 

A.D 

S 

?2 

D.        H. 

D.        H 

D.        H. 

D.        H.  $ 

1777 

20      12A 

10       1  A 

19       2M 

18       3A  S 

§  55 

1778 

10       9M 

9     10A 

8     11M 

7     12A  J; 

s 

^ 

S56 

1779 

29       7M 

28       8  A 

27       9M 

26        9A  S 

V       • 

1780 

17       3A 

17       4M 

15       5A 

S 
15       6M  $ 

S  58 

1781 

6     12A 

6       1  A 

5       2M 

4       3A  S 

u 

1782 

25      10A 

25     11M 

23      12  A 

S 

23        OA  $ 

S60 

1783 

15       6M 

14       7A 

13       8M 

12        9A  S 

S61 

c 

1784 

3        3A 

3       4M 

1        5A 

1       6M  $ 

30       6A  $ 

?62 

1785 

22        1A 

22       2M 

20        3  A 

20       3M  S 

$63 

1786 

11       9A 

11     10M 

9     HA 

9       OA  $ 

S  64 

1787 

1       6M 
30       7A 

30       8M 

28       9A 

28       9M  S 

$65 

1788 

19      4M 

18       5A 

17       6M 

16       7A$ 

S  66 

1789 

8       1  A 

8       2M 

6       3A 

6       4M  S 

S 

S 

$  67 

1790 

29     10M 

26     11  A 

25       OA 

24     12  A  $ 

S68 

1791 

16       7A 

16       8M 

14       9A 

14     10M  S 

$  69 

1792 

5       4A 

4       5A 

3       6M 

2»r    A     S 
•'*•   ^ 

S70 

1793 

24       2M 

23       3  A 

22       4M 

21       4A  S 

h- 

1794 

13     10M 

12     11  A 

11       OA 

S  72 

1795 

2       7A 

2       8M 
31        9A 

30     10M 

29     10AS 

$73 

1796 

20       4A 

20       5M 

18       6A 

18       7M  > 

S  74 

1797 

0      1M 

9       2A 

8        3M 

7       4A^ 

S 

S 

$  75 

1798 

28     11  A 

28        OA 

27        1M 

26        1A  $ 

In 

1799 

18       8M 

17        9A 

16     10M 

15      HAS 

<    1|1800|  6       4A 

6       5M 

4       6A 

4       7M  ^ 

412  Of  the  Division  of  Time. 


388.  The  cycle  of  Easter,  also  called  the  Dionysian 
'Per*od>  is  a  revolution  of  532  years,  found  by  mul- 
tiplying the  solar  cycle  28  by  the  lunar  cycle  19.  If 
the  new  Moons  did  not  anticipate  upon  this  cycle, 
Easter-day  would  always  be  the  Sunday  next  after 
the  first  full  Moon  which  follows  the  21st  of  March. 
But  on  account  of  the  above  anticipation,  §  422. 
to  which  no  proper  regard  was  had  before  the  late 
alteration  of  the  style,  the  ecclesiastic  Easter  has  se- 
veral times  been  a  week  different  from  the  true  East- 
er within  this  last  century  :  which  inconvenience  is 
now  remedied  by  making  the  table  which  used  to 
find  Easter  for  ever,  in  the  Common  Prayer  Book, 
of  no  longer  use  than  the  lunar  difference  from  the 
new  style  will  admit  of. 

Number  389.  The  earliest  Easter  possible  is  the  22d  of 
of  direc-  March,  the  latest  the  25th  of  April.  Within  these 
limits  are  35  days,  and  the  number  belonging  to 
each  of  them  is  called  the  number  of  direction;  be- 
cause thereby  the  time  of  Easter  is  found  for  any 
given  year.  To  find  the  number  of  direction,  ac- 
cording to  the  new  style,  enter  Table  V.  following 
this  chapter,  with  the  complete  hundreds  of  any 
given  year  at  the  top,  and  the  years  thereof  (if  any) 
below  a  hundred  at  the  left  hand  ;  and  where  the  co- 
lumns meet  is  the  Dominical  letter  for  the  given 
year.  Then  enter  Table  I.  with  the  complete  hun- 
dreds of  the  same  year  at  the  left  hand,  and  the 
years  below  a  hundred  at  the  top;  and  where  the 
columns  meet  is  the  golden  number  for  the  same 
year.  Lastly,  enter  Table  II.  with  the  Dominical 
letter  at  the  left  hand,  and  golden  number  at  the  top  ; 
and  where  the  columns  meet  is  the  number  of  direc- 
tion for  that  year;  which  number  added  to  the  21st 
day  of  March,  shews  on  what  day,  either  of  March 
or  April,  Easter-  Sunday  falls  in  that  year.  Thus 
the  Dominical  letter  new  style  for  the  year  1757  is  B, 
(Table  V.J  and  the  golden  number  is  10,  (Table  I.) 
by  which  in  Table  II.  the  number  of  direction  is 


Of  the  Division  of  Time.  4 13 

found  to  be  20;  which  reckoning  from  the  21st  of  TO  find 

the  trOe 
Easter. 


March,  ends  on  the  10th  of  April,  that  is,  Easter- tbe  trfle 


Sunday,  in  the  year  1757.  N.  B.  There  are  always 
two  Dominical  letters  to  the  leap-year,  the  first  of 
which  takes  place  to  the  24th  of  February,  the  last 
for  the  following  part  of  the  year. 

390.  The  first  seven  letters  of  the  alphabet  are 
commonly  placed  in  the  annual  almanacs,  to  shew 
on  what  days  of  the  week  the  days  of  the  months 
fall  throughout  the  year.  And  because  one  of  those 
seven  letters  must  necessarily  stand  against  Sunday, 
it  is  printed  in  a  capital  form,  and  called  the  Domi-  Dominical 
nical  letter :  the  other  six  being  inserted  in  small Ietter* 
characters,  to  denote  the  other  six  days  of  the  week. 
Now,  since  a  common  Julian  year  contains  365 
days,  if  this  number  be  divided  by  7  (the,  number 
of  days  in  a  week)  there  will  remain  one  day.  If 
there  had  been  no  remainder,  it  is  plain  the  year 
would  constantly  begin  on  the  same  day  of  the  week. 
But  since  1  remains,  it  is  as  plain  that  the  year  must 
begin  and  end  on  the  same  day  of  the  week ;  and 
therefore  the  next  year  will  begin  on  the  day  follow- 
ing. Hence,  when  January  begins  on  Sunday,  A 
is  the  Dominical  or  Sunday  letter  for  that  year : 
then,  because  the  next  year  begins  on  Monday,  th« 
Sunday  will  fall  on  the  seventh  day,  to  which  is  an- 
nexed the  seventh  letter  G,  which  therefore  will  be 
the  Dominical  letter  for  all  that  year:  and  as  the 
third  year  will  begin  on  Tuesday,  the  Sunday  wil£ 
fall  on  the  sixth  day ;  therefore  F  will  be  the  Sunday 
letter  for  that  year.  Whence  it  is  evident,  that  the 
Sunday  letters  will  go  annually  in  a  retrograde  order 
thus,  G,  F,  E,  D,  C,  B,  A.  And  in  "the  course 
of  seven  years,  if  they  were  all  common  ones,  the 
same  days  of  the  week  and  Dominical  letters  would 
return  to  the  same  days  of  the  months.  But  because 
there  are  366  days  in  a  leap-year,  4f  this  number  be 
divided  by  7,  there  will  remain  two  days  over  and 
above  the  52  weeks  of  which  the  year  consists. 


41 4  Of  the  Division  of  Time. 

And  therefore,  if  the  leap-year  begins  on  Sunday, 
it  will  end  on  Monday  ;  and  the  next  year  will  be- 
gin on  Tuesday,  the  first  Sunday  whereof  must 
fall  on  the  sixth  of  January,  to  which  is  annexed  the 
letter  F,  and  not  G,  as  in  common  years.  By 
this  means,  the  leap-year  returning  every  fourth 
year,  the  order  of  the  Dominical  letters  is  interrupt- 
ed ;  and  the  series  cannot  return  to  its  first  state  till 
after  four  times  seven,  or  28  years  ;  and  then  the 
same  days  of  the  months  return  in  order  to  the  same 
days  of  the  week  as  before. 

To  find  391.  To  find  the  Dominical  letter  for  any  year 
the  .  .  either  before  or  after  the  Christian  (era.  In  Table 
cal  "letter.  ^-  or  IV.  ^or  o Id  style,  or  V.  for  new  style,  look 
for  the  hundreds  of  years  at  the  head  of  the  table, 
and  for  the  years  below  a  hundred  (to  make  up  the 
given  year)  at  the  left  hand;  and  where  the  columns 
meet,  you  have  the  Dominical  letter  for  the  year  de- 
sired. Thus,  suppose  the  Dominical  letter  be  re- 
quired for  the  year  of  CHRIST  1758,  new  style,  I 
look  for  1700  at  the  head  of  Table  V.  and  for  58  at 
the  left  hand  of  the  same  table ;  and  in  the  angle  of 
meeting,  I  find  A,  nhich  is  the  Dominical  letter  for 
that  year.  If  it  was  wanting  for  the  same  year  old 
style,  it  would  be  found  by  Table  IV.  to  be  D. 
But  to  find  the  Dominical  letter  for  any  given  year 
before  CHRIST,  subtract  one  from  that  year,  and 
then  proceed  in  all  respects  as  just  now  taught,  to 
find  it  by  Table  III.  Thus,  suppose  the  Domini- 
cal letter  be  required  fof  the  585th  year  before  the 
first  year  of  C  H  R  i  s  T,  look  for  500  at  the  head  of  Ta- 
ble III.  and  for  84  at  the  left  hand ;  in  the  meeting 
of  these  col umns  you  will  find  FE,  which  were  the 
Dominical  letters  for  that  year,  and  shew  that  it  was 
a  leap-}  ear ;  because  leap-year  has  always  two  Do- 
minical letters. 

TO  find  392-  To  find  the  day  of  the  month  answering  to 
the  day  amj  day  of  the  week,  or  the  day  of  the  week  an- 
severing  to  any  day  of  the  month,  for  any  year  past 


Of  the  Divhwn  of  Time,  4L5 

jf  to  come.  Having  found  the  Dominical  letter  for 
the  given  year,  enter  Table  VI,  with  the  Dominical  / 
letter  at  the  head;  and  under  it,  all  the  days  in  that 
column  are  Sundays,  in  the  divisions  of  the  months; 
the  next  column  to  the  right  hand  are  Mondays;  the 
next,  Tuesdays ;  and  so  on,  to  the  last  column  un- 
der G;  from  which  go  back  to  the  column  under  A, 
and  thence  proceed  toward  the  right  hand  as  before. 
Thus,  in  the  year  1757,  the  Dominical  letter  new 
style  is  B,  in  Table  V  ;  then,  in  Table  VI,  all  the 
days  under  B  are  Sundays  in  that  year,  viz.  the  2d, 
9th,  16th,  23d,  and  3Oth  of  January  and  October  ; 
the  6th,  13th,  2Oth,  and  27th  of  February,  March, 
and  November;  the  3d,  lOth,  and  17th  of  yf/>r/7and 
July,  together  with  the  31st  of  July  ;  and  so  on,  to 
the  foot  of  the  column.  Then,  of  course,  all  the 
days  under  Care  Mondays,  namely,  the  3d,  10th, 
&c.  of  January  and  October  ;  and  so  of  all  the  rest 
in  that  column.  If  the  day  of  the  week  answering 
to  any  day  of  the  mon?h  be  required,  it  is  easily  had 
from  the  same  table  by  the  letter  that  stands  at  the 
top  of  the  column  in  which  the  given  day  of  the 
month  is  found.  Thus,  the  letter  that  stands  over 
the  28th  of  May  .is  A  ;  and  in  the  year  58.5  before 
CHRIST,  the  Dominical  letters  were  found  to  be 
F,  E,  §  391  ;  which  being  a  leap-year,  and  E 
taking  place  from  the  24th  of  February  to  the  end 
of  that  year,  shews,  by  the  table,  that  the  25th  of 
May  was  on  a  Sunday ;  and  therefore  the  28th  must 
have  been  on  a  Wednesday  ;  for  when  E  stands  for 
Sunday,  F  must  stand  for  Monday,  G  for  Tues- 
day, &c.  Hence,  as  it  is  said  that  the  famous  eclipse 
of  the  Sun  foretold  by  THALES,  by  which  a  peace 
"tfas  brought  about  between  the  Medes  and  Lydians, 
happened  on  the  28th  of  May,  in  the  585th  year 
before  CHRIST,  it  fell  on  a  Wednesday. 

393.  From  the  multiplication  of  the  solar  cycle  juiian 
of  28  years,  into  the  lunar  cycle  of  19  years,  and  the  period. 
Roman  indiction  of  1 5  years,  arises  the  great  Julian 
3G 


416          Of  the  Times  of  the  Birth  and  Death  of  CHRIST, 

period,  consisting  of  7980  years,  which  had  its  be- 
ginning 764  years  before  Strauchius's  supposed  year 
uf  the  creation  (for  no  later  could  all  the  three 
cycles  begin  together),  and  it  is  not  yet  completed : 
and  therefore  it  includes  all  other  cycles,  periods, 
and  seras.  There  is  but  one  year  in  the  whole  pe- 
riod that  has  the  same  numbers  for  the  three  cycles 
of  which  it  is  made  up  :  and  therefore,  if  historians 
had  remarked  in  their  writings  the  cycles  of  each 
year,  there  had  been  no  dispute  about  the  time  of 
any  action  recorded  by  them. 

TO  find  the      394.  The  Dionysian  or  vulgar  sera  of  CHRIST'S 
period*.^15  birth  was  about  the  end  of  the  year  of  the  Julian  pe- 
riod 4713  ;  and  consequently  the  first  year  of  his 
age,  according  to  that  account,  was  the  4714th  year 
of  the  said  period*     Therefore,  if  to  the  current 
year  of  CHRIST  we  add  4713,  the  sum  will  be  the 
year  of  the  Julian  period.   So  the  year  1 757  will  be 
found  to  be  the  6470th  year  of  that  period*  Or,  to 
find  the  year  of  the  Julian  period  answering  to  any 
given  year  before  the  first  year  of  CHRIST,  subtract 
the  number  of  that  given  year  from  4714,  and  the 
remainder  will  be  the  Julian  period.     Thus,  the 
year  585  before  the  first  year  of  CHRIST   (which 
was  the  584th  before  his  birth)  was  the  41 29th  year 
of  the  said  period.  Lastly,  to  find  the  cycles  of  the 
Sun,  Moon,  and  indiction,  for  any  given  year  of  this 
period,  divide  the  given  year  by  28,  19,  and  15; 
And  the     tne  tnree  remainders  will  be  the  cycles  sought,  and 
cycles  of    the  quotients  the  numbers  of  cycles  elapsed  since 
that  year.  the  beginning  of  the  period.    So  in  the  above  47 14th 
year  of  the  Julian  period,  the  cycle  of  the  Sun  was 
10,  the  cycle  of  the  Moon  2,  and  the  cycle  of  indic- 
tion 4;  the  solar  cycle  having  run  through  168 
courses,  the  lunar  248,  and  the  indiction  314. 
The  true        395.  The  vulgar  sera  of  CHRIST'S  birth  was 
CHRIST'S  never  settled  till  the  year  527,  when  Dionysius  Exi- 
birtb,       guus,  a  Roman  abbot,  fixed  it  to  the  end  of  the 
4713th  year  of  the  Julian  period,  which  was  four 


Of  the  Times  of  the  Birth  and  Death  of  CHRIST.          417 

years  too  late. — For  our  SAVIOUR  was  born  before 
the  death  of  Herod,  who  sought  to  kill  him  as  soon 
as  he  heard  of  his  birth.  And  according  to  the  tes- 
timony of  Josephus  (B.  xvii.  ch.  8.)  there  was  an 
eclipse  of  the  Moon  at  the  time  of  Herod's  last  ill- 
ness  ;  which  eclipse  appears  by  our  astronomical  ta- 
bles to  have  been  in  the  year  of  the  Julian  period 
47 1O,  March  13th,  at  3  hours  past  midnight,  at  Je- 
rusalem. Now  as  our  SAVIOUR  must  have  been 
born  some  months  before  Herod's  death,  since  in  the 
interval  he  was  carried  into  Egypt,  the  latest  time  in 
which  we  can  fix  the  true  sera  of  his  birth  is  about 
the  end  of  the  4709th  year  of  the  Julian  period. 

There  is  a  remarkable  prophecy  delivered  to  us 
in  the  ninth  chapter  of  the  book  of  Daniel,  which, 
from  a  certain  epoch,  fixes  the  time  of  restoring  the 
state  of  the  Jews,  and  of  building  the  walls  of  Jeru- 
salem, the  coming  of  the  MESSIAH,  his  death,  and 
the  destruction  of  Jerusalem. — But  some  parts  of 
this  prophecy  (Ver.  25.)  are  so  injudiciously  pointed 
in  our  English  translation  of  the  Bible,  that,  if  they 
be  read  according  to  those  stops  of  pointing,  they 
are  quite  unintelligible. — But  the  learned  Dr.  Pri- 
deaux,  by  altering  these  stops,  makes  the  sense  very 
plain  ;  and  as  he  seems  to  me  to  have  explained  the 
whole  of  it  better  than  any  other  author  I  have  read 
on  the  subject,  I  shall  set  down  the  whole  of  the 
prophecy  according  as  he  has  pointed  it,  to  shew  in 
what  manner  he  has  divided  it  into  four  different 
parts. 

Ver.  24.  Seventy  weeks  are  determined  upon  thy 
People,  and  upon  thy  holy  City,  to  finish  the  Trans- 
gression, and  to  make  an  end  of  Sins,  and  to  make 
reconciliation  for  Iniquity,  and  to  bring  in  everlast- 
ing Righteousness,  and  to  seal  up  the  Vision,  and  the 
Prophecy,  and  to  anoint  the  most  holy.  Ver.  25, 
Know  therefore  and  understand,  that  from  the  going 
forth  of  the  Commandment  to  restore  and  to  build  Je- 
rusalem unto  the  MESSIAH  the  Prince  shall  be  seven 


418          Of  the  Times  of  the  Birth  and  Death  of  CHRIST. 

weeks  and  three-score  and  two  weeks,  the  street  shall 
be  built  again,  and  the  wall  even  in  troublous  times. 
Ver.  2f>.  And  after  three-score  and  two  weeks  shall 
MESSIAH  be  cut  off,  but  not  for  himself,  and  the  peo- 
ple of  the  Prince  that  shall  come,  shall  destroy  the 
City  and  Sanctuary,  and  the  end  thereof  shall  be 
with  a  Flood,  and  unto  the  end  of  the  war  desola- 
tions are  determined.  Ver.  27.  And  he  shall  con- 
firm the  covenant  with  many  for  one  week,  and  in 
the  midst*  of  the  week  he  shall  cause  the  sacrifice 
and  the  oblation  to  cease,  and  for  the  overspreading 
of  abominations  he  shall  make  it  desolate  even  until 
the  Consummation,  and  that  determined  shall  be  pour- 
ed upon  the  desolate. 

This  commandment  was  given  to  Ezra  by  Artax- 
erxes  Longimanus,  in  the  seventh  year  of  that  king's 
reign  (Ezra,  ch.  vii.  ver.  i  1 — 26).  Ezra  began  the 
work,  which  was  afterwards  accomplished  by  Nehe- 
miah  :  in  which  they  met  with  great  opposition  and 
trouble  from  the  Samaritans  and  others,  during  the 
first  seven  weeks,  or  49  years. 

From  this  accomplishment  till  the  time  when 
CHRIST'S  messenger,  John  the  Baptist,  began  to 
preach  the  Kingdom  of  the  MESSIAH,  62  weeks,  or 
434  years. 

From  thence  to  the  beginning  of  CHRIST'S  pub* 
lie  ministry,  half  a  week,  or  3y  years. 

And  from  thence  to  the  death  of  CHRIST,  half  a 
week,  or  3y  years;  in  which  half-week  he  preached, 
and  confirmed  the  covenant  of  the  Gospel  with  many. 

In  all,  from  the  going  forth  of  the  commandment 
till  the  Death  of  CHRIST,  70  weeks,  or  490  years* 

And,  lastly,  in  a  very  striking  manner,  the  pro- 
phecy foretels  what  should  come  to  pass  after  the  ex- 
piration of  the  seventy  weeks  ;  namely,  the  Destruc- 
tion of  the  City  and  Sanctuary  by  the  people  of  the 
Prince  that  was  to  come  ;  which  were  the  Roman 

*  The  Doctor  says,  that  this  ought  to  be  rendered  the 
half  part  of  the  week)  v&tthe  midst. 


Of  the  Times  of  the  Birth  and  Death  of  CHRIST.         41 9 

armies,  under  the  command  of  Titus  their  prince, 
who  came  upon  Jerusalem  as  a  torrent,  with  their 
idolatrous  images,  which  were  an  abomination  to 
the  Jews,  and  under  which  they  marched  against 
them,  invaded  their  land,  and  besieged  their  holy 
city,  and  by  a  calamitous  war,  brought  such  utter 
destruction  upon  both,  that  the  Jews  have  never 
been  able  to  recover  themselves,  even  to  this  day. 

Now,  both  by  the  undoubted  canon  of  Ptolemy, 
and  the  famous  tera  of  Nabonassar,  the  beginning 
of  the  seventh  year  of  the  reign  of  Artaxerxes  Lon- 
gimanus,  king  of  Persia,  (who  is  called  Ahasuerus 
in  the  book  of  Esther,}  is  pinned  down  to  the 
4^56th  year  of  the  Julian  period,  in  which  year  he 
gave  Ezra  the  above-mentioned  ample  commission: 
from  which,  count  490  years  to  the  death  of 
CHRIST,  and  it  will  carry  the  same  to  the  4746th 
year  of  the  Julian  period. 

Our  Saturday  is  the  Jewish  Sabbath :  and  it  is 
plain  from  St.  Mark,  ch.  xv.  ver.  42,  and  St.  Luke, 
ch.  xxiii.  ver.  54,  that  CHRIST  was  crucified  on  a 
Friday,  seeing  the  crucifixion  was  on  the  day  next 
before  the  Jewish  Sabbath. — And  according  to  St. 
John,  ch.  xviii.  ver.  28,  on  the  day  that  the  Passover 
was  to  be  eaten,  at  least  by  many  of  the  Jews. 

The  Jews  reckoned  their  months  by  the  Moon, 
and  their  years  by  the  apparent  revolution  of  the 
Sun  :  and  they  ate  the  Passover  on  the  14th  day  of 
the  month  of  Nisan,  which  was  the  first  month  of 
their  year,  reckoning  from  the  first  appearance  of 
the  new  Moon,  which  at  that  time  of  the  year  might 
be  on  the  evening  of  the  day  next  after  the  change, 
if  the  sky  was  clear.  So  that  their  1 4th  day  of  the 
month  answers  to  our  fifteenth  day  of  the  Moon, 
on  which  she  is  full. — Consequently,  the  Passover 
was  always  kept  on  the  day  of  full  Moon. 

And  the  full  Moon  at  which  it  was  kept,  was  that 
one  which  happened  next  after  the  vernal  equinox. 
— For  Josef  hus  expressly  $&y$^Antiq,  B.  iii.  ch.  10.) 


420          Of  the  Times  of  the  Birth  and  Death  of  CHRIST. 

c  The  Passover  was  kept  on  the  14th  day  of  the 
"month  of  Nisan,  according  to  the  Moon,  when  the 
"  Sun  was  in  Aries." — And  the  Sun  always  enters 
Aries  at  the  instant  of  the  vernal  equinox  ;  which, 
in  our  Saviour's  time,  fell  on  the  22d  day  of  March. 
The  dispute  among  chronologers  about  the  year 
of  CHRIST'S  death  is  limited  to  four  or  five  years  at 
most. — But,  as  we  have  shewn  that  he  was  cruci- 
fied on  the  day  of  a  Pascal  full  Moon,  and  on  a 
Friday,  all  that  we  have  to  do,  in  order  to  ascer- 
tain the  year  of  Kis  death,  is  only  to  compute  in 
which  of  those  years  there  was  a  Passover  full 
Moon  on  a  Friday. — For,  the  full  Moons  anticipate 
eleven  days  every  year  (12  lunar  months  being  so 
much  short  of  a  solar  year),  and  therefore,  once 
in  every  three  years  at  least,  the  Jews  were  oblig- 
ed to  set  their  Passover  a  whole  month  for- 
warder than  it  fell  by  the  course  of  the  Moon,  on 
the  year  next  before,  in  order  to  keep  it  at  the  full 
Moon  next  after  the  equinox ;  therefore  there 
could  not  be  two  Passovers  on  the  same  nominal 
day  of  the  week  within  the  compass  of  a  few 
neighbouring  years.  And  I  find  by  calculation, 
the  only  Passover  full  Moon  that  fell  on  a  Friday, 
for  several  years  before  or  after  the  disputed  year 
of  the  crucifixion,  was  on  the  3d  day  of  April,  in 
the  4746th  year  of  the  Julian  period,  which  was 
the  4POth  year  after  Ezra  received  the  above-men- 
tioned commission  from  Ariaxerxes  Longimanus, 
according  to  Ptolemy9 s  canon,  and  the  year  in  which 
the  MESSIAH  was  to  be  cut  off,  according  to  the 
prophecy,  reckoning  from  the  going  forth  of  that 
commission  or  commandment :  and  this  490th  year 
was  the  33d  year  of  our  SAVIOUR'S  age,  reckoning 
from  the  vulgar  asra  of  his  birth  ;  but  the  37th, 
reckoning  from  the  true  asra  thereof. 

And,  when  we  reflect  on  what  the  Jews  told  him, 
some  time  before  his  death  (John  viii.  57.)  "  thou. 
"  art  not  yet  fifty  years  old,"  we  must  confess  that 
it  should  seem  much  likelier  to  have  been  said  to  a 


Of  the  Times  of  the  Birth  and  Death  of  CHRIST.          42  i 

person  near  forty  than  to  one  but  just  turned  of 
thirty.  And  we  may  easily  suppose  that  St.  Luke 
expressed  himself  only  in  round  numbers,  when 
he  said  that  Christ  was  baptized  about  the  SOtbyear 
of  his  age,  when  he  began  his  public  ministry;  as  our 
SAVIOUR  himself  did,  when  he  said  he  should  lie 
three  days  and  three  nights  In  the  grave. 

The  4746th  year  of  the  Julian  period,  which  we 
have  astronomically  proved  to  be  the  year  of  the 
crucifixion,  was  the 4th  year  of  the  202d  Olympiad; 
in  which  year,  Phlegon,  a  heathen  writer,  tells  us, 
there  was  the  most  extraordinary  eclipse  of  the  Su?t 
that  ever  was  seen.  But  I  find  by  calculation,  that 
there  could  be  no  total  eclipse  of  the  Sun  at  Jerusa- 
lem^ in  a  natural  way,  in  that  year. — So  that  what 
Phlegon  here  calls  an  eclipse  of  the  Sun  seems  to 
have  been  the  great  darkness  for  three  hours  at  the 
time  of  our  SAVIOUR'S  crucifixion,  as  mentioned 
by  the  Evangelists  :  a  darkness  altogether  superna- 
tural, as  the  Moon  was  then  in  the  side  of  the  hea- 
vens opposite  to  the  Sun  ;  and  therefore  could  not 
possibly  darken  the  Sun  to  any  part  of  the  Earth. 

396.  As  there  are  certain  fixed  points  in  the  hea- 
vens from  which  astronomers  begin  their  computa- 
tions, so  there  are  certain  points  of  time  from  which 
historians  begin  to  reckon  ;  and  these  points,  or 
roots  of  time,  are  called  aras  or  epochs.  The  most 
remarkable  aras  are,  those  of  the  creation,  theGra^ 
Olympiads,  the  building  of  Rome,  the  ara  of  Nabo* 
nassar,  the  death  of  Alexander,  the  birth  of  CHRIST, 
the  Arabian  Hegira,  and  the  Persian  Tesdegird  :  all 
which,  together  with  several  others  of  less  note, 
have  their  beginnings  in  the  fqllowing  table  fixed 
to  the  years  of  the  Julian  period,  to  the  age  of  the 
world  at  those  times,  and  to  the  years  before  and 
after  the  year  of  CHRIST'S  birth. 


(     422     ) 


A  Table  of  remarkable  Mras  and  Events. 


1.  The  Creation  of  the  World 

2.  The  Deluge,  or  Noah's  Flood 

3.  The  Assyrian  Monarchy  founded  by  Nimrod 

4.  The  Birth  of  Abraham  .... 

5.  The  Destruction  of  Sodo?n  and  Gomorrah 

6.  The  Beginning  of  the  Kingdom  of  Athens  by  Cecrops 

7.  Moses  receives  the  Ten  Commandments 

8.  The  Entrance  of  the  Israelites  into  Canaan 

9.  The  Arganautic  Expedition 
10.  The  Destruction  of  Troy 

\  1.  The  Beginning  of  King  David's  Reign 

12.  The  Foundation  of  Solomon's  Temple 

13.  Lycurgus  forms  his  excellent  Laws 

14.  Arbaces,  the  first  King  of  the  Medea 

15.  Mandaucus,  the  second          .... 

1 6.  Sosarmus,  the  third  ..... 

1 7.  The  Beginning  of  the  Olympiads 

18.  Attica,  the  fourth  King  of  the  Medes     . 

19.  The  Catonian  Efiocha  of  the  Building  of  Rome 

20.  The  JEra  of  jYabonassar         .... 

21.  The  Destruction  of  Samaria  by  Salmaneser 

22.  The  first  Eclipse  of  the  Moon  on  Record 

23.  Cardicea,  the  fifth  King  of  the  Medes 

24.  Phraortes,  the  sixth  .... 

25.  Cyaxares,  the  seventh  .... 

26.  The  first  Babylonish  Captivity  by  Nebuchadnezzar 

27.  The  long  War  ended  between  the  Medea  and  Lydiam 

28.  The  second  Babylonish  Captivity,  and  Birth  of  Cyrus 

29.  The  Destruction  of  Solomon's  Temple 

30.  Nebuchadnezzar  struck  with  Madness 

31.  Daniel's  Vision  of  the  four  Monarchies 

32.  Cyrus  begins  to  reign  in  the  Persian  Empire 

33.  The  Battle  of  Marathon        .... 

34.  Artaxerxes  Longimanus  begins  to  reign 

5.  The  Beginning  of  Daniel's  seventy  Weeks  of  Years 
The  Beginning  of  the  Pelojionnesian  War     . 
Alexander's  Victory  at  Arbela 

His  Death 

The  Captivity  of  100,000  Jews  by  King  Ptolemy 
.  The  Colossus  of  Rhodes  thrown  down  by  an  Earthquake 
Antiochus  defeated  by  Ptolemy  Philofiater 
The  famous  ARCHIMEDES  murdered  at  Syracuse 
Jason  butchers  the  Inhabitants  of  Jerusalem 
Corinth  plundered  and  burnt  by  Consul  Mummius 
Julius  Caesar  invades  Britain 
He  corrects  the  Calendar 
Is  killed  in  the  Senate-House 


»>3 

36 
37 
38 
39 
40 
41, 
42 
43 
44 
45 
46 
47 


Lilian 
Period. 

Y.ofthe 
World. 

Befott. 
Christ 

706 

0 

4007 

2362 

1656 

2351 

2537 

1831 

2176 

2714 

2008 

1999 

2816 

2110 

i897 

3157 

2451 

1556 

3222 

2516 

1491 

3262 

2556 

1451 

3420 

2714 

1293 

3504 

2798 

1209 

3650 

2944 

1063 

3701 

2995 

1012 

3829 

3103 

884 

3838 

3132 

875 

3865 

3159 

848 

3915 

3209 

798 

3938 

3232 

775 

3945 

3239 

768 

3961 

3255 

752 

3967 

3261 

746 

3992 

3286 

721 

3993 

3287 

720 

3996 

3290 

717 

4058 

3352 

655 

4080 

3374 

633 

4107 

3401 

606 

4111 

3405 

602 

4114 

34C8 

599 

4125 

3419 

588 

4144 

3438 

569 

4158 

3452 

555 

4177 

3471 

536 
490 
464 

4223 

4249 

3517 
3543 

4256 

3550 

457 

4282 

3576 

431 

4383J3677 

330 

4390 

3684 

323 

4393 

3687 

320 

•  449  1 

3875 

222 

4496 

3790 

217 

4506 

3800 

207 

4543 

3837 

170 

4567 

3851 

146 

4659 

3953 

54 

4677 

3961 

46 

4671 

3965 

43 

A  Table  of  remarkable  Mr  as  ana  Events.         423 


48. 
49. 
50. 
51. 

52. 

53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 

65. 
66, 


Herod  made  King  of  Judea     ---<-. 
Anthony  defeated  at  the  Battle  of  Actium  - 
Agrifijia  builds  the  Pantheon  at  Rome 
The  true  ^.RA  of  CHRIST'S  Birth 
The  Death  of  Herod 


The  Dyonisian  or  vulgar  J£RA  of  CHRIST'S  Birth 
The  true  year  of  his  Crucifixion      .... 
The  Destruction  of  Jerusalem      -     -     -     -     - 
Adrian  builds  the  Long  Wall  in  Britain     -     - 
Constantius  defeats  the  Picts  in  Britain     -     - 

The  Council  of  Mice 

The  Death  of  Constantine  the  Great  -  -  - 
The  Saxons  invited  into  Britain  .  •  -  * 
The  Arabian  Hegira  --..-... 
The  Death  of  Mohammed  the  pretended  Prophet 
The  Persian  Yesdegird  ----.-- 
The  Sun,  Moon,  and  all  the  Planets  in  Libra, 

Sefit.  14,  as  seen  from  the  Earth 
The  Art  of  Printing  discovered        -     -     -     - 
The  Reformation  begun  by  Martin  Luther     - 


Julian 

Y.ofthe 

Before 

Period. 

World. 

Christ. 

4673 

3967 

40 

4683 

3977 

30 

4688 

3982 

25 

4709 

4003 

4 

4710 

4004 

3 

After 

Christ. 

4713 

4007 

0 

4746 

4040 

33 

4783 

4077 

70 

4833 

4127 

120 

5019 

4313 

306 

5038 

4332 

325 

5050 

4344 

337 

5158 

4452 

445 

5335 

4629 

622 

5343 

4637 

630 

5344 

4638 

631 

5899 

5193 

1186 

6153 

5447 

1440 

6230 

5524 

1517 

In  fixing  the  year  of  the  creation  to  the  706th  Age  of 
year  of  the  Julian  Period,  which  was  the  4007th the  wor.ld 
year  before  the  year  of  CHRIST'S  birth,  T  have  fol-  U1 
lowed  Mr.  Bedford  in  his  Scripture- Chronology, 
printed  A.  D.  1730,  and  Mr.  Kennedy,  in  a  work 
of  the  same  kind,  printed  A.  D.  1762. — Mr.  Bed- 
ford takes  it  only  for  granted  thai  the  world  was 
created  at  the  time  of  the  autumnal  equinox ;  but 
Mr.  Kennedy  affirms  that  the  said  equinox  was  at 
the  noon  of  the  fourth  day  of  the  creation -week,  and 
that  the  moon  was  then  24  hours  past  her  opposition 
to  the  Sun. — If  Moses  had  told  us  the  same  things, 
we  should  have  had  sufficient  data  for  fixing  the  ara 
of  the  creation ;  but  as  he  has  been  silent  on  these 
points,  we  must  consider  the  best  accounts  of  chro- 
nologers  as  entirely  hypothetical  and  uncertain. 

3K 


424 


Tables  of  Time. 


S  TABLE  I.   Shewing  the  Golden  Number  (which  is  the  same  both 
IJ       the  Old  and  New  Styles)  from  the  Christian  JEra  to  4.  D.  380. 

S ! „ — , 

s  Years  less  than  an  Hundred. 


1 


k                                                                 W 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

5* 

S  Hundreds 
S    Of 

19 
38 

20 
39 

21 
40 

22 
41 

23 
42 

24 
43 

25 

14 

26 
4., 

27 

28 

47 

29 
•8 

30 

49 

31 

50 

32 
51 

33 

52 

34 
53 

35 
54 

36 
55 

37  S 
56? 

s 

S  Years. 

57 

76 

58 
77 

59 
78 

60 
79 

61 

80 

62 
81 

63 
82 

64 

t>3 

65 

84 

66 

85 

67 
86 

68 
87 

69 
88 

70 
89 

71 
90 

72 
91 

73 
92 

74 
93 

Si 

S 

95 

96 

97 

98 

99 

$ 

5  c 

i900 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

^9$ 

$  loo 

2000 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

1 

2 

3 

4 

5S 

>  200 

2100 

i  1 

12 

13 

14 

15 

16 

17 

18 

19 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10  S 

S  300 

2200 

16 

17 

18 

19 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15  S 

Ij  400 

2300 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

1 

Jj  500 

.400 

7 

8 

9 

10 

11 

12 

13 

14 

15 

If 

17 

18 

19 

1 

2 

3 

4 

5 

?  600 

4500 

12 

13 

14 

15 

16 

17 

18 

19 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

us 

>  700 

.;600 

17 

18 

19 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16  c 

?  800 

2700 

g 

4 

5 

6 

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Tables  of  Time. 


425 


'  Tables  of  Time. 


S  TABLE  III.  Shelving  the  Dominical  Letters,  Ola !  S 
S  Style,  for  4200  Years  before  the  Christian  ;Era.  £ 


5  Bcf.  Christ 

Hundreds  of  Years                  Jj 

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0 

100 

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600  J» 

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Tables  of  Time. 

S  TABLE  IV.    Shewing  the  Dominical  Letters^  Old\ 
S       Style,' for  4200  Years  after  the  Christian  &ra.   \ 


£  Alt.  Christ 

Hundreds  of  Years.                   Jj 

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428 


Tables  of  Time. 


S  TABLE  V.  The  Dominical  Letter^  S 
S  New  Style,  for  4000  Years  after  <J 
^  the  Christian  JEra.  *  S 


£  After  Chr. 

Hundreds  of  Years.   S 

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Tables  of  Time. 


429 


S       the  Months,  for  both  Styles,  by  the  J 
?       Dominical  Letters.                           s 

ij  Week  Days. 

A 

1 
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430  The  ORRERY  described. 


CHAP.  XXII. 


A  Description  of  the  Astronomical  Machinery  serv- 
ing to  explain  and  illustrate  the  foregoing  Part 
of  this  Treatise. 


Frontin     39~  r  I  ^HE  ORRERY.  This  machine  shews  the 

f  he  Title-  JL     motions  of  the  Sun,  Mercury,  Venus, 

page.  The  Earth,  and  Moon  ;  and  occasionally,  the  superior 

'RKERY.  p}anets>  Mars,  Jupiter,  and  Saturn,  may  be  put  on; 

Jupiter's  four  satellites  are  moved  round  him  in 

their  proper  times  by  a  small  winch  ;  and  Saturn 

has  his  five  satellites,  and  his  ring,  which  keeps  its 

parallelism  round  the  Sun  ;  and  by  a  lamp  put  in 

the  Sun's  place,  the  ring  shews  all  the  phases  de- 

scribed in  the  204th  article. 

The  Sun.       In  the  centre,  No.  1.  represents  the  SUN,  sup- 

ported by  its  axis  inclining  almost  8  degrees  from 

the  axis  of  the  ecliptic  ;  and  turning  round  in  25-j 

days  on  its  axis,  of  which  the  north  pole  inclines 

toward  the  8th  degree  of  Pisces  in  the  great  ecliptic 

The  eclip-  (No.  II.),  whereon  the  months  and  days  are  en- 

tic.          graven  over  the  signs  and  degrees  in  \vhich  the  Sun 

appears,  as  seen  from  the  Earth,  on.  the  diffe 

days  of  the  year. 

Mercury.  The  nearest  planet  (No.  2.)  to  the  Sun  is  Mi 
cury,  which  goes  round  him  in  87  days  23  hours, 
or  87ff  diurnal  rotations  of  the  Earth  ;  but  has  no 
motion  round  its  axis  in  the  machine,  because  the 
time  of  its  diurnal  motion  in  the  heavens  is  not 
known  to  ns. 

Venus.          The  next  planet  in  order  is  Venus  (No.  3.)  which 
performs  her  annual  course  in  224  days  17  hours; 
and  turns  round  her  axis  in  24  days  8  hours,  or 
in  24|  diurnal  rotations  of  the  Earth.     Her  axi 
inclines  75  degrees  from  the  axis  of  the  ecliptic 
and  her  north  pole  inclines  toward  the  20th  de 
gree  of  Aquarius,  according  to  the  observations  o 


sun 
rrent 

VIer. 


The  ORRERY  described*  431 

Bianchini.     She  shews  all  the  phenomena  described 
from  the  30th  to  the  44th  article  in  chap.  1. 

Next  without  the  orbit  of  Venus  is  the  Earth,  TheEarth. 
(No.   4.)  which  turns  round  its  axis,  to  any  fixed 
point  at  a  great  distance,  in  23   hours  56  minutes 
4  seconds,  of  mean  solar  time  (\  221,  &  seq.),  but 
from  the  sun  to  the  Sun  again  in  24  hours  of  the 
same  time.     No.   6.  is  a  sidereal  dial- plate  under  the 
Earth  ;  and  No.   7.  a  solar  dial- plate  on  the  cover  of 
the  machine.     The  index  of  the  former  shews  side- 
!  real,  and  of  the  latter,  solar  time ;  and  hence,  the  for- 
\  mer  index  gains  one  entire  revolution  on  the  latter 
-•}  every  year,  as  365  solar  or  natural  days  contain  366 
sidereal  days,  or  apparent  revolutions  of  the  stars.  In 
the  time  that  the  Earth  makes  36  5£  diurnal  rotations 
on  its  axis,  it  goes  once  round  the  Sun  in  the  plane 
of  the  ecliptic ;  and  always  keeps  opposite  to  a  mov- 
ing index  (No.  10.),  which  shews  the  Sun's  apparent 
daily  change  of  place,  and  also  the  days  of  the  months. 
The  Earth  is  half  covered  vuth  a  black  cap,  to 
divide  the  apparently-enlightened  half  next  the  Sun 
from  the  other  half)  which  when  turned  away  from  him. 
is  in  the  dark.     The  edge  of  the  cap  represents  the 
circle  bounding  light  and  darkness,  and  shews  at  what 
time  the  Sun  rises  and  sets  to  all  places  throughout  the 
year.  The  Earth's  axis  inclines  231  degrees  from  the 
j  axis  of  the  ecliptic,  the  north  pole  inclines  toward  the 
beginning  of  Cancer,  and  keeps  its  parallelism  through- 
out its  annual  course,  $  48,  202;   so  that  in  summer 
the  northern  parts  of  the  Earth  inclines  toward  the 
Sun,  and  in  winter  declines  from  him  :    by  which 
means  the  different  lengths  of  days  and  nights,  and 
the  cause  of  the  various  seasons,  are  demonstrated 
to  sight. 

There  is  a  broad  horizon,  to  the  upper  side  of 
which  is  fixed  a  meridian- semicircle  in  the  north  and 
south  points,  graduated  on  both  sides  from  the  h  >ri- 
zon  to  90°  in  the  zenith,  or  vertical  point.  The  cage 

31 


432  The  ORRERY  described. 

of  the  horizon  is  graduated  from  the  east  and  west  to 
the  south  and  north  points,  and  within  these  divisions 
are  the  points  of  the  compass.  From  the  lower  side 
of  this  thin  horizon -plate,  stand  out  four  small  wires, 
to  which  is  fixed  a  twilight-circle  18  degrees  from  the 
graduated  side  of  the  horizon  all  round/  This  hori- 
zon may  be  put  upon  the  Earth  (when  the  cap  is  taken 
away),  and  rectified  to  the  latitude  of  anyplace:  and 
then,  by  a  small  wire  called  the  solar  ray,  which  may 
be  put  on  so  as  to  proceed  directly  from  the  Sun's 
centre  toward  the  Earth's,  but  to  come  no  farther  than 
almost  to  touch  the  horizon.  The  beginning  of  twi- 
light, time  of  sun-rising,  with  his  amplitude,  meridi- 
an-altitude, time  of  setting,  amplitude  then,  and  end 
of  twilight,  are  shewn  for  every  day  of  the  year,  at 
that  place  to  which  the  horizon  is  rectified. 

TheMoon  ^^e  Moon  (No.  5.)  goes  round  the  Earth,  from 
*  between  it  and  any  fixed  point  at  a  great  distance,  in 
27  days  7  hours  43  minutes,  or  through  all  the  signs 
and  degrees  of  her  orbit ;  which  is  called  her  periodi- 
cal revolution :  but  she  goes  round  from  the  Sun  to 
the  Sun  again,  or  from  change  to  change,  in  29  days 
12  hours  45  minutes,  which  is  her  synodical  revolu- 
tion ;  and  in  that  time  she  exhibits  all  the  phases  al- 
ready described,  $  255, 

When  the  above-mentioned  horizon  is  rectified  to 
the  latitude  of  any  given  place,  the  times  of  the  Moon's 
rising  and  setting,  together  with  her  amplitude,  are 
shewn  to  that  place  as  well  as  the  Sun's,  and  all  the 
various  phenomena  of  the  harvest-moon,  §  273,  & 
seq.  are  made  obvious  to  sight. 

The  nodes.  The  Moon's  orbit  (No.  9.)  is  inclined  to  the 
ecliptic  (No.  11.),  one  half  being  above,  and  the 
other  below  it.  The  nodes,  or  points  at  0  and  0,  lie 
in  the  plane  of  the  ecliptic,  as  described  §  317,  318, 
and  shift  backward  through  all  its  signs  and  degrees 
in  18f  years,  The  degrees  of  the  Moon's  latitude,  to 


The  ORRERY  described. 

the  highest  at  N  L  (north  latitude),  and  lowest  at  S 
L  (south  latitude),  are  engraven  jpoth  ways  from  her 
nodes  at  0  and  0 ;  and  as  the  Moon  rises  and  falls  in 
her  orbit  according  to  its  inclination,  her  latitude  and 
distance  from  her  nodes  are  shewn  for  every  day ; 
having  first  rectified  her  orbit  so  as  to  set  the  nodes 
to  their  proper  places  in  the  ecliptic :  and  then,  as 
they  come  about  at  different,  and  almost  opposite, 
times  of  the  year,  §  319,  and  point  twice  toward  the 
Sun ;  all  the  eclipses  may  be  shewn  for  hundreds  of 
years  (without  any  new  rectification)  by  turning  the 
machinery  backward  for  time  past,  or  forward  for 
time  to  come.  At  17  degrees  distance  from  each 
node,  on  both  sides,  is  engraven  a  small  sun ;  and 
at  12  degrees  distance,  a  small  moon;  which  shew 
the  limits  of  solar  and  lunar  eclipses,  §317:  and 
when,  at  any  change,  the  moon  falls  between  either 
of  these  suns  and  the  node,  the  Sun  will  be  eclipsed 
on  the  day  pointed  to  by  the  annual  index  (No.  10.), 
and  as  the  Moon  has  then  north  or  south  latitude, 
one  may  easily  judge  whether  *hat  eclipse  will  be  vi- 
sible in  the  northern  or  southern  hemisphere ;  espe- 
cially as  the  Earth's  axis  inclines  toward  the  Sun  or 
declines  from  him  at  that  time.  And  when  at  any 
full,  the  Moon  falls  between  either  of  the  little  moons 
and  node,  she  will  be  eclipsed,  and  the  annual  index 
shews  the  day  of  that  eclipse.  There  is  a  circle  of 
29|  equal  parts  (No.  8.)  on  the  cover  of  the  machine, 
on  which  an  index  shews  the  days  of  the  Moon's  age. 

A  semi-ellipsis  and  semicircle  are  fixed  to  an  el-  Plate  Ix, 
liptical  ring,  which  being  put  like  a  cap  upon  theFlff'X* 
Earth,  and  the  forked  part  F  upon  the  Moon,  shews 
the  tides  as  the  Earth  turns  round  within  them,  and 
they  are  led  round  it  by  the  Moon.     When  the  dif- 
ferent places  come  to  the  semi-ellipsis  daEbB,  they 
have  tides  of  flood  :  and  when  they  come  to  the  se- 
micircle CED,  they  have  tides  of  ebb,  §  304,  305  ; 


434  The  ORRERY  described. 

the  index  on  the  hour-circle  (No.  7.)  shewing  the 
times  of  these  phenomena. 

There  is  a  jointed  wire,  of  which  one  end  being 
put  into  a  hole  in  the  upright  stem  that  holds  the 
Earth's  cap,  and  the  wire  laid  into  a  small  forked 
piece  which  may  be  occasionally  put  upon  Venus  or 
Mercury,  shews  the  direct  and  retrograde  motions  of 
these  two  planets,  with  their  stationary  times  and 
places  as  seen  from  the  Earth. 

The  whole  machinery  is  turned  by  a  winch  or 
handle  (No.  !£.),  and  is  so  easily  moved,  that  a  clock 
might  turn  it  without  any  danger  of  stopping. 

To  give  a  plate  of  the  wheel- work  of  this  machine 
would  answer  no  purpose,  because  many  of  the 
wheels  lie  so  behind  others,  as  to  hide  them  from 
sight  in  any  view  whatsoever. 

Another  398.  Another  ORRERY.  In  this  machine,  which 
ORRERY.  js  ^le  simplest  I  ever  saw,  for  shewing  the  diurnal 
™"teyL  and  annual  motions  of  the  Earth,  together  with  the 
motion  of  the  Moon  and  her  nodes,  A  and  B  are 
two  oblong  square  pkt.es  held  together  by  four  up- 
right pillars;  of  which  three  appear  atjT,  g9  andg*  2. 
Under  the  plate  A  is  an  endless  screw  on  the  axis  of 
the  handle  6,  which  works  in  a  wheel  fixed  on  the 
same  axis  with  the  double-grooved  wheei  E;  and  on 
the  top  of  this  axis  is  fixed  the  toothed  wheel  f,  which 
turns  the  pinion  k,  on  the  top  of  whose  axis  is  the 
pinion  k  2,  which  turns  another  pinion  b  2,  and  that 
turns  a  third,  which  being  fixed  on  a  2,  the  axis  of 
the  Earth  £/,  turns  it  round,  and  the  earth  with  it : 
this  last  axis  inclines  in  an  angle  of  23-|  degrees.  The 
supporter  X  2,  in  which  the  axis  of  the  earth  turns, 
is  fixed  to  the  moveable  plate  C. 

In  the  fixed  plate  B,  beyond  H,  is  fixed  the  strong 
wire  cf,  on  which  hangs  the  sun  7\  so  as  it  may  turn 
round  the  wire.  To  this  sun  is  fixed  the  wire  or  so- 
lar ray  Z,  which  (as  the  earth  Z/turns  round  its  axis) 
points  to  all  the  places  that  the  Sun  passes  vertically 
over,  every  day  of  the  year.  The  earth  is  half  co- 


The  ORRERY  described.  435 


f  ered  with  a  black  cap  a,  as  in  the  former  Orrery,  for 
dividing  the  day  from  the  night ;  and  as  the  different 
places  come  out  trom  below  the  edge  of  the  cap,  or 
go  in  below  it,  they  shew  the  times  of  sun-rising  and 
setting  every  day  of  the  year.  This  cap  is  fixed  on 
the  wire  6,  which  has  a  forked  piece  C  turning  round 
the  wire  d:  and,  as  the  earth  goes  round  the  sun,  it 
carries  the  cap,  wire,  and  solar  ray  round  him ;  so 
that  the  solar  ray  constantly  points  toward  the  earth's 
centre. 

On  the  axis  of  the  pinion  k  is  the  pinion  m,  which 
turns  a  wheel  on  the  cock  or  supporter  72,  and  on  the 
axis  of  this  wheel  nearest  n  is  a  pinion  (hid  from 
view)  under  the  plate  C,  which  pinion  turns  a  wheel 
that  carries  the  moon  /Around  the  earth  U ;  the  moon's 
axis  rising  and  falling  in  the  socket  W,  which  is  fix- 
ed to  the  triangular  piece  above  2* ;  and  this  piece  is 
fixed  to  the  top  of  the  axis  of  the  last- mentioned 
wheel.  The  socket  TFis  slit  on  the  outermost  side : 
and  in  this  slit  the  two  pins  near  Y,  fixed  in  the  moon's 
axis,  move  up  and  down ;  one  of  them  being  above 
the  inclined  plane  FJf,  and  the  other  below  it.  By 
this  mechanism,  the  moon  V  moves  round  the  earth 
T  in  the  inclined  orbit  ^,  parallel  to  the  plane  of  the 
ring  YX;  of  which  the  descending  node  is  at  Jf,  and 
the  ascending  node  opposite  to  it,  but  hid  by  the  sup- 
porter X  2. 

The  small  wheel  E  turns  the  large  wheels  D  and 
F9  of  equal  diameters,  by  cat-gut  strings  crossing 
between  them :  and  the  axes  of  these  two  wheels  are 
cranked  at  G  and  H9  above  the  plate  £.  The  up- 
right stems  of  these  cranks  going  through  the  plate 
C,  carry  it  over  and  over  the  fixed  plate  JB,  with  a 
motion  which  carries  the  earth  U  round  the  sun  Ty 
keeping  the  earth's  axis  always  parallel  to  itself,  or 
still  inclining  toward  the  left  hand  of  the  plate ;  and 
shewing  the  vicissitudes  of  seasons,  as  described  in 
the  tenth  chapter.  As  the  earth  goes  round  the  sun , 


436  The  ORRERY  described. 

the  pinion  k  goes  round  the  wheel  i,  for  the  axis  of 
k  never  touches  the  fixed  plate  .Z?,  but  turns  on  a 
wire  fixed  into  the  plate  C. 

On  the  top  of  the  crank  G  is  an  index  L,  which 
goes  round  the  circle  m  2  in  the  time  that  the  earth 
goes  round  the  sun,  and  points  to  the  days  of  the 
months ;  which,  together  with  the  names  of  the  sea- 
sons, are  marked  in  this  circle. 

This  index  has  a  small  grooved  wheel  L  fixed 
upon  it,  round  which,  and  the  plate  Z,  goes  a  cat- 
gut string  crossing  between  them ;  and  by  this  means 
the  moon's  inclined  plane  YX,  with  its  nodes,  is 
*  turned  backward,  for  shewing  the  times  and  returns 
of  eclipses,  §  310,  320. 

The  following  parts  of  this  machine  must  be  con- 
sidered as  distinct  from  those  already  described. 

Toward  the  right  hand,  let  S  be  the  earth  hung 
on  the  wire  e,  which  is  fixed  into  the  plate  B ;  and 
let  0  be  the  moon  fixed  on  the  axis  AT,  and  turning 
round  within  the  cap  P,  in  which,  and  in  the  plate 
C,  the  crooked  wire  Q  is  fixed.  On  the  axis  M  is 
also  fixed  the  index  K,  which  goes  round  a  circle  h 
2,  divided  into  29£  equal  parts,  which  are  the  days 
of  the  Moon's  age :  but  to  avoid  confusion  in  the 
scheme,  it  is  only  marked  with  the  numeral  figures 
1234,  for  the  quarters.  As  the  crank  H  carries 
this  moon  round  the  earth  S  in  the  orbit  £,  she  shews 
all  her  phases  by  means  of  the  cap  P  for  the  different 
days  of  her  age,  which  are  shewn  by  the  index  K; 
this  index  turning  just  as  the  moon  0  does,  demon- 
strates her  turning  round  her  axis,  as  she  still  keeps 
the  same  side  toward  the  earth  £,  §  262. 

At  the  other  end  of  the  plate  CT,  a  moon  N  goes 
round  an  earth  R  in  the  orbit  p.  But  this  moon's 
axis  is  stuck  fast  into  the  plate  C  at  £  2,  so  that  nei- 
ther moon  nor  axis  can  turn  round  ;  and  as  this  moon 
goes  round  her  earth,  she  shews  herself  all  round  to 
it ;  which  proves,  that  if  the  Moon  was  seen  all  round 


The  CALCULATOR  described.  437 

from  the  Earth  in  a  lunation,  she  could  not  turn  round 
her  axis. 

N.-  B.  If  there  were  only  the  two  wheels  D  and 
.F,  with  a  cat- gut  string  over  them,  but  not  crossing 
between  them,  the  axis  of  the  earth  U  would  keep 
its  parallelism  round  the  Sun  71,  and  shew  all  the  sea- 
sons ;  as  I  sometimes  make  these  machines  :  and  the 
moon  0  would  go  round  the  earth  S,  shewing  her 
phases  as  above ;  as  likewise  would  the  moon  Aground 
the  earth  R;  but  then  neither  could  the  diurnal  mo- 
tion of  the  earth  £7  on  its  axis  be  shewn,  nor  the  mo- 
tion  of  the  moon  Ground  the  earth. 

399.  In  the  year  1746  I  contrived  a  very  simple  The  CAL- 
machine,  and  described  its  performance  in  a  small CULATOR' 
Treatise^  upon  the  Phenomena  of  the  Harvest- Moon, 
published  in  the  year  1747.     I  improved  it  soon 
after,  by  adding  another  wheel,  and  called  it  The 
Calculator.  It  may  be  easily  made  by  any  gentleman 
who  has  a  mechanical  genius. 

The  great  flat  ring  supported  by  twelve  pillars,  and  Plate 
on  which  the  twelve  signs  with  their  respective  de- «.  ", 
grees  are  laid  down,  is  the  ecliptic ;  nearly  in  the  lg* 
centre  of  it  is  the  sun  St  supported  by  the  strong 
crooked  wire  /;  and  from  the  sun  proceeds  a  wire  W+ 
called  the  solar  rat/,  pointing  toward  the  centre  of 
the  earth  E,  which  is  furnished  with  a  moveable  ho- 
rizon Ht  together  with  a  brazen  meridian,  and  quad- 
rant of  altitude.  R  is  a  small  ecliptic,  whose  plane 
coincides  with  that  of  the  great  one,  and  has  the  like 
signs  and  degrees  marked  upon  it ;  and  is  supported 
by  two  wires  D  and  Z),  which  are  put  into  the  plane 
PP9  but  may  be  taken  off  at  pleasure.  As  the  earth 
goes  round  the  sun,  the  signs  of  this  small  circle 
keep  parallel  to  themselves,  and  to  those  of  the  great 
ecliptic.  When  it  is  taken  off,  and  the  solar  ray  W 
drawn  farther  out,  so  as  almost  to  touch  the  horizon 
ff,  or  the  quadrant  of  altitude,  the  horizon  being  rec* 


438  The  CALCULATOR  described. 

tified  to  any  given  latitude,  and  the  earth  turned  round 
its  axis  by  hand,  the  point  of  the  wire  IV  shews  the 
sun's  declination  in  passing  over  the  graduated  brass 
meridian,  and  his  height  at  any  given  time  upon  the 
quadrant  of  altitude,  together  with  his  azimuth,  or 
point  of  bearing  upon  the  horizon  at  that  time  ;  and 
likewise  his  amplitude,  and  time  of  rising  and  setting 
by  the  hour-index,  for  any  day  of  the  year  that  the 
annual-index  U  points  to  in  the  circle  of  months  be- 
low the  sun.  M  is  a  solar-index  or  pointer  support- 
ed by  the  wire  Ly  which  is  fixed  into  the  knob  K: 
the  use  of  this  index  is  to  shew  the  Sun's  place  in  the 
ecliptic  every  day  in  the  year ;  for  it  goes  over  the 
signs  and  degrees  as  the  index  U  goes  over  the 
months  and  days ;  or  rather,  as  they  pass  under  the 
index  U,  in  moving  the  cover- plate  with  the  earth  and 
its  furniture  round  the  sun ;  for  the  index  Z7is  fixed 
tight  on  the  immoveable  axis  in  the  centre  of  the  ma- 
chine, ^is  a  knob  or  handle  for  moving  the  earth 
round  the  sun,  and  the  moon  round  the  earth. 

As  the  earth  is  carried  round  the  sun,  its  axis  con- 
stantly keeps  the  same  oblique  direction,  or  parallel 
to  itself,  §  48,  202,  shewing  thereby  the  different 
lengths  of  days  and  nights  at  different  times  of  the 
year,  with  all  the  various  seasons.  And,  in  one  an- 
nual revolution  of  the  earth,  the  moon  M  goes  12-| 
times  round  it  from  change  to  change,  having  an  oc- 
casional provision  for  shewing  her  different  phases. 
The  lower  end  of  the  moon's  axis  bears  by  a  small 
friction- wheel  upon  the  inclined  plane  J*,  which  causes 
the  moon  to  rise  above  and  sink  below  the  ecliptic  R 
in  every  lunation ;  crossing  it  in  her  nodes,  which  shift 
backward  through  all  the  signs  and  degrees  of  the 
said  ecliptic,  by  the  retrograde  motion  of  the  in- 
clined plane  71,  in  18  years  and  225  days.  On 
this  plane  the  degrees  and  parts  of  the  moon's 
north  and  south  latitude  are  laid  down  from  both 


The  CALCULATOR  described.  439 

the  nodes,  one  of  which,  viz.  the  descending  node, 
appears  at  0,  by  DN  above  B  ;  the  other  node  be- 
ing hid  from  sight  on  this  plane  by  the  plate  PP ; 
and  from  both  nodes,  at  proper  distances,  as  in  the 
other  Orrery,  the  limits  of  eclipses  are  marked,  and 
all  the  solar  and  lunar  eclipses  are  shewn  in  the  same 
manner,  for  any  given  year  within  the  limits  of  6000, 
either  before  or  after  the  Christian  asra.  On  the 
plate  that  covers  the  wheel- work,  under  the  Sun  S, 
and  round  the  knob  K,  are  astronomical  tables,  by 
which  the  machine  may  be  rectified  to  the  begin- 
ning of  any  given  year  within  these  limits,  in  three 
or  tour  minutes  of  time ;  and  when  once  set  right, 
may  i>e  turned  backward  for  300  years  past,  or  for- 
ward for  as  many  to  come,  without  requiring  any 
new  rectification.  There  is  a  method  for  its  adding 
up  the  29th  of  February  every  fourth  year,  and 
allowing  only  28  days  to  that  month  for  every  other 
three ;  but  ail  this  being  performed  by  a  particular 
manner  of  cutting  the  teeth  of  the  wheels,  and 
dividing  the  month-circle,  too  long  and  intricate  to 
be  described  here,  I  shall  only  shew  how  these 
motions  may  be  performed  near  enough  tor  com- 
mon use,  by  wheels  with  grooves  and  cat-gut  strings 
round  them ;  only  here  I  must  put  the  operator  in 
mind,  that  the  groove  are  to  be  made  sharp-bottom- 
ed, (not  round)  to  keep  the  strings  from  slipping. 

The  moon's  axis  moves  up  and  down  in  the 
socket  jV,  fixed  into  the  bar  0,  (which  carries  her 
round  the  earth)  as  she  rises  above  or  sinks  below 
the  ecliptic;  and  immediately  below  the  inclined 
plane  T  is  a  flat  circular  plate  (between  Fand  T] 
on  which  the  different  eccentricities  of  the  Moon's 
orbit  are  laid  down ;  and  likewise  her  mean  anomaly 
and  elliptic  equation,  by  which  her  true  place  may 
be  very  nearly  found  at  any  time.  Below  this  apo- 
gee-plate, which  shews  the  anomaly,  &c.  is  a 
circle  F  divided  into  29£  equal  parts,  which  are  the 

(  3K) 


.440  The  CALCULATOR  described. 

« 

days  of  the  Moon's  age :  and  the  forked  end  A  of 
the  index  AB  (Fig.  II.)  may  be  put  into  the  apo- 
gee-part of  this  plate  ;  there  being  just  such  another 
index  to  put  into  the  inclined  plane  T  at  the  as- 
cending node :  and  then  the  curved  points  B  of  these 
indexes  shew  the  direct  motion  of  the  apogee,  and 
retrograde  motion  of  the  nodes  through  the  ecliptic 
R,  with  their  places  in  it  at  any  given  time.  As  the 
inoon  M  goes  round  the  earth  E^  she  shews  her 
place  every  day  in  the  ecliptic  7t!,  and  the  lower  end 
of  her  axis  shews  her  latitude  and  distance  from  her 
node  on  the  inclined  plane  Y1,  also  her  distance  from 
her  apogee  and  perigee,  together  with  her  mean 
anomaly,  the  then  eccentricity  of  her  orbit,  and  her 
elliptic  equation,  all  on  the  apogee-plate,  and  the 
day  of  her  age  in  the  circle  Y  of  29|  equal  parts, 
for  every  day  of  the  year,  pointed  out  by  the  annual 
index  Uin  the  circle  of  months. 

Having  rectified  the  machine  by  the  tables  for 
the  beginning  of  any  year,  move  the  earth  and 
moon  forward  by  the  knob  K,  until  the  annual 
index  comes  to  any  given  day  of  the  month,  then 
stop,  and  not  only  all  the  above  phenomena  may 
be  shewn  for  that  day,  but  also,  by  turning  the 
earth  round  its  axis,  the  declination,  azimuth, 
amplitude,  altitude  of  the  Moon  at  any  hour,  and 
the  times  of  her  rising  and  setting,  are  shewn  by 
the  horizon,  quadrant  of  altitude,  and  hour-index. 
And  in  moving  the  earth  round  the  sun,  the  days 
of  all  the  new  and  full  moons  and  eclipses  in  any 
given  year  are  shewn.  The  phenomena  of  the 
harvest-moon,  and  those  of  the  tides,  by  such  a  cap 
as  that  in  plate  IX.  Fig.  10.  put  upon  the  earth  and 
moon,  together  with  the  solution  of  many  problems 
not  here  related,  are  made  conspicuous. 

The  easiest,  though  not  the  best,  way,  thai  I  can 
instruct  any  mechanical  person  to  malge  the  wheel-* 

fc-V 


772? CALCULATOR  described.  441 

work  of  such  a  machine,  is  as  follows:  which  is  the 
way  that  I  made  it,  before  I  thought  of  numbers 
exact  enough  to  make  it  worth  the  trouble  of  cut- 
ting teeth  in  the  wheels. 

Fig.  3d  of  Plate  VIII.  is  a  section  of  this  ma-    PLATE 
chine ;  in  which  ABCD  is  a  frame  of  wood  held  to-  Fi  VII1IIf 
gether  by  four  pillars  at  the  corners ;  two  of  which   ^' 
appear  at  AC  and  BD.     In  the  lower  plate  CD  of 
this  frame  are  three  small  friction-wheels,  at  equal 
distances  from  each  other ;  two  of  them  appearing 
at  e  and  e.     As  the  frame  is  moved  round,  these 
wheels  run  upon  the  fixed  bottom -plate  ££,  which 
supports  the  whole  work. 

In  the  centre  of  this  last-mentioned  plate  is  fixed 
the  upright  axis  GFFf,  and  on  the  same  axis  is 
fixed  the  wheel  HHH>  in  which  are  four  grooves^ 
/,  X,  k,  jLj  of  clifierent  diameters.  In  these  grooves 
are  cat-gut  strings  going  also  round  the  separate 
wheels  M,  JV,  O,  and  P. 

The  wheel  Mis  fixed  on  a  solid  spindle  or  axis, 
the  lower  pivot  of  which  turns  at  R  in  the  under 
plate  of  the  moveable  frame  ABCD ;  and  on  the 
upper  end  of  this  axis  is  fixed  the  plate  oo  (which 
is  PP,  under  the  earth,  in  Fig;  1.^,  and  to  this 
plate  is  fixed  at  an  angle  of  23^  degrees  inclination, 
the  dial-plate  below  the  earth  T ;  on  the  axis  of 
which,  the  index  q  is  turned  round  by  the  earth. 
This  axisj  together  with  the  wheel  M^  and  plate  oo, 
keep  their  parallelism  in  going  round  the  sun  S. 

On  the  axis  of  the  wheel  M  is  a  moveable 
socket j  on  which  the  small  wheel  JV  is  fixed,  and 
on  the  upper  end  of  this  socket  is  put  on  tight  (but 
so  as  it  may  be  occasionally  turned  by  hand)  the 
bar  ZZ  (viz.  the  bar  0  in  Fig.  1.)  which  carries 
the  moon  772  round  the  earth  7",  by  the  socket  n^ 
fixed  into  the  bar.  As  the  moon  goes  round  the 
earth,  her  axis  rises  and  falls  in  the  socket  n  ;  be- 
cause, on  the  lower  end  of  her  axis,  which  is  turned 
inward,  there  is  a  small  friction- wheel  $  running 


442  The  CALCULATOR  described. 

on  the  inclined  plane  X  (which  is  Tin  Fig.  1.),  and 
so  causes  the  moon  alternately  to  rise  above  and 
sink  below  the  little  ecliptic  VV (R  in  Fig.  1.)  in 
every  lunation. 

On  the  socket  or  hollow  axis  of  the  wheel  Ar, 
there  is  another  socket,  on  which  the  wheel  0  is 
fixed;  and  the  moon's  inclined  plane  X  is  put 
tightly  on  the  upper  end  of  this  socket,  not  on  a 
square,  but  on  a  round,  that  it  may  be  occasionally 
set  by  hand  without  wrenching  the  wheel  or  axle. 

Lastly,  on  the  hollow  axis  of  the  wheel  O  is  an- 
other socket,  on  which  is  fixed  the  wheel  P,  and  on 
the  upper  end  of  this  socket  is  put  on  tightly  the 
apogee-plate  Y(that  immediately  below  Tin  Fig.  1.) 
All  these  axles  turn  in  the  upper  plate  of  the  move- 
,  .able  frame  at  Q  /  which  plate  is  covered  with  the 
thin  plate  cc  (screwed  to  it),  whereon  are  the  fore- 
mentioned  tables  and  month- circle  in  Fig.  1. 

The  middle  part  of  the  thick  fixed  wheel  HHH 
is  much  broader  than  the  rest  of  it,  and  comes  out 
between  the  wheels  M  and  O  almost  to  the  wheel 
JV.  To  adjust  the  diameters  of  the  grooves  of  this 
fixed  wheel  to  the  grooves  of  the  separate  wheels 
M,  A",  0,  and  P,  so  as  they  may  perform  their 
motion  in  their  proper  times,  the  following  method 
must  be  observed. 

The  groove  of  the  wheel  M,  which  keeps  the 
parallelism  of  the  earth's  axis,  must  be  precisely 
of  the  same  diameter  as  the  lower  groove  /  of  the 
fixed  wheel  HHH;  but,  when  this  groove  is  so 
•well  adjusted  as  to  shew,  that  in  ever  so  many  an- 
nual, revolutions  of  the  Earth,  its  axis  keeps  its 
parallelism,  as  may  be  observed  by  the  solar  ray 
7F(Fig.  1.)  always  coming  precisely  to  the  same 
degree  oi  the  small  ecliptic  R  at  the  end  of  every 
annual  revolution,  when  the  index  AT  points  to  the 
like  degree  in  the  great  ecliptic ;  then,  with  the 
edge  ol  a  thin  file,  give  the  groove  of  the  wheel  M 
a  small  rub  all  round,  and,  by  that  means  lessening 


The  CALCULATOR  described.  443 

the  diameter  of  the  groove  perhaps  about  the  20th 
part  of  a  hair's  breadth,  it  will  cause  the  earth  to 
shew  the  precession  of  the  equinoxes ;  which,  in 
many  annual  revolutions,  will  begin  to  be  sensible, 
as  the  earth's  axis  deviates  slowly  from  its  paralle- 
lism, §  246,  toward  the  antecedent  signs  of  the 
ecliptic. 

The  diameter  of  the  groove  of  the  wheel  TV, 
which  carries  the  moon  round  the  earth,  must  be 
to  the  diameter  of  the  groove  X,  as  a  lunation  is  to 
a  year,  that  is,  as  29$  to  365|. 

'The  diameter  of  the  groove  of  the  wheel  0, 
which  turns  the  inclined  plane  X  with  the  moon's 
nodes  backward,  must  be  to  the  diameter  of  the 
groove  £,  as  20  to  18ff£.  And, 

Lastly,  the  diameter  of  the  groove  of  the  wheel 
P,  which  carries  the  moon's  apogee  forward,  must 
be  to  the  diameter  of  the  groove  .L,  as  70  to  62. 

But  after  all  this  nice  adjustment  of  the  grooves 
to  the  proportional  times  of  their  respective  wheels 
turning  round,  and  which  seems  to  promise  very 
well  in  theory,  there  will  still  be  found  a  necessity 
of  a  farther  adjustment  by  hand ;  because  proper 
allowance  must  be  made  for  the  diameters  of  the 
cat- gut  strings :  and  the  grooves  must  be  so  adjust- 
ed by  hand,  as,  that  in  the  time  the  earth  is  moved 
once  round  the  sun,  the  moon  must  perform  12 
sy  nodical  revolutions  round  the  earth,  and  be  almost 
11  days  old  in  her  13th  revolution.  The  inclined 
plane  with  its  nodes  must  go  once  round  backward  t 
through  all  the  signs  and  degrees  of  the  small  eclip- 
tic in  18  annual  revolutions  of  the  earth,  and  225 
days  over.  And  the  apogee-plate  must  go  once 
round  forward,  so  as  its  index  may  go  over  all  the 
signs  and  degrees  of  the  small  ecliptic  in  eight 
years  (or  so  many  annual  revolutions  of  the  earth) 
and  312  days  over. 

N  B.  The  string  which  goes  round  the  grooves 
X  and  JV,  for  the  moon's  motion,  must  cross  .be- 
tween these  wheels;  but  all  the  rest, of  the 


R1UM 


444  The  COMETARIUM  described. 

go  in  their  respective  grooves,  IMk,  O,  and  LP, 
without  crossing. 

The  400.     The  COMETARIUM.     This  curious  ma- 

COMETA-  chine  shews  the  motion  of  a  comet,  or  eccentric 
body  moving  round  the  Sun,  describing  equal  areas 
in  equal  times,  \  152,  and  may  be  so  contrived  as 
to  shew  such  a  motion  for  any  degree  of  eccen- 
tricity. It  was  invented  by  the  late  Dr.  DESAGU- 

LIERS. 

The  dark  elliptical  groove  round  the  letters 
abcdefghiklm  is  the  orbit  of  the  comet  Y:  this 
comet  is  carried  round  in  the  groove,  according  to 
tne  or(*er  °f  letters»  by  the  wire  W  fixed  in  the  sun 
S,  and  slides  on  the  wire  as  it  approaches  nearer 
to,  or  recedes  farther  from,  the  sun  ;  being  nearest 
of  all  in  the  perihelion  c,  and  farthest  in  the  aphe- 
lion g.  The  areas  aSb,  bSc,  cSd,  &c.  or  contents 
of  these  several  triangles,  are  all  equal :  and  in  every 
turn  of  the  winch  JV",  the  comet  Y  is  carried  over 
one  of  these  areas :  consequently,  in  as  much  time 
as  it  moves  from  f  to  g,  or  from  g  to  /z,  it  moves 
from  772  to  a,  or  from  a  to  b ;  and  so  of  the  rest, 
being  quickest  of  all  at  tz,  and  slowest  at  g.  Thus 
the  comet's  velocity  in  its  orbit  continually  decreases 
from  the  perihelion  a  to  the  aphelion  gv  and  increases 
in  the  same  proportion  from  g  to  a. 
.  The  elliptical  orbit  is  divided  into  12  equal  parts 
or  signs,  with  their  respective  degrees,  and  so  is 
the  circle  nopqrstn,  which  represents  a  great  circle 
in  the  heavens,  and  to  which  the  comet's  motion  is 
referred  by  a  small  knob  on  the  point  of  the  wire 
W.  While  the  comet  moves  from  f  to  g  in  its 
orbit,  it  appears  to  move  only  about  5  degrees  in 
this  circle,  as  is  shewn  by  the  small  knob  on  the 
end  of  the  wire  W;  but  in  the  like  time,  as  the 
comet  moves  from  m  to  #,  or  from  a  to  by  it  appears 
to  describe  the  large  space  tn  or  no  in  the  heavens, 
either  of  which  spaces  contains  120  degrees,  or  four 
signs.  Were  the  eccentricity  of  its  orbit  greater. 


The  COMETARIUM  described.  445 

die  greater  still  would   be  the  difference   of  its 
motion,  and  vice  versa. 

ABCDEFGH1KLMA  is  a  circular  orbit  for 
shewing  the  equal  motion  of  a  body  round  the  sun 
S,  describing  equal  areas  ASB,  BSC,  &c.  in  equal 
times  with  those  of  the  body  Y  in  its  elliptical  orbit, 
above  mentioned  ,  but  with  this  difference,  that  the 
circular  motion  describes  the  equal  arcs  AB,  BC, 
&c.  in  the  same  equal  times  that  the  elliptical  mo- 
tion describes  the  unequal  arcs  ab,  be,  &c. 

Now,  suppose  the  two  bodies  Fand  1  to  start 
from  the  points  a  and  A  at  the  same  moment  of 
time,  and  each  having  gone  round  its  respective 
orbit,  to  arrive  at  these  points  again  at  the  same 
instant,  the  body  F  will  be  forwarder  in  its  orbit 
than  the  body  1  all  the  way  from  a  to  g,  and  from 
A  to  G ;  but  1  will  be  forwarder  than  Y  through 
all  the  other  half  of  the  orbit ;  and  the  difference  is  t 
equal  to  the  equation  oi%  the  body  Fin  its  orbit. 
At  the  points  a,  A,  and  g,  6r,  that  is  in  the  perihe- 
lion and  aphelion,  they  will  be  equal ;  and  then  the 
equation  vanishes.  This  shews  why  the  equation 
of  a  body  moving  in  an  elliptic  orbit,  is  added  to 
the  mean  or  supposed- circular  motion,  from  the 
perihelion  to  the  aphelion;  and  subtracted,  from  the 
aphelion  to  the  perihelion,  in  bodies  moving  round 
the  Sun,  or  from  the  perigee  to  the  apogee,  and 
from  the  apogee  to  the  perigee,  in  the  Moon's 
motion  round  the  Earth,  according  to  the  precepts 
in  the  353d  article ;  only  we  are  to  consider,  that 
when  motion  is  turned  into  time,  it  reverses  the 
titles  in  the  table  of  The  Moorfs  elliptic  Equal  ion. 

This  motion  is  performed  in  the  following  man-  plate  /r 
ner  by  the  machine.    ABC  is  a  wooden  bar  (in  the  Fig.  v. 
box  containing  the  wheel- work),  above  which  are 
the  wheels  Z?  ii  $  E  ;  and  below  it  the  efl  p       j^iatf  s 
FF  and  GO;, each  plate  being  fixed  on  ;.n  axis  in 
one  of  its  focuses,  at  E  and  K:  and  the  wheel  E  is 
fixed  oil  the  same  axis  with  the  plate  FF,    These 


446  ,      The  COMETARIUM  described. 

plates  have  grooves  round  their  edges  precisely  of 
equal  diameters  to  one  another,  and  in  these  grooves 
is  the  cat-gut  strings  gg,  gg,  crossing  between  the 
plates  at  h.  On  H  (the  axis  of  the  handle  or  winch 
JVin  Fig.  4th)  is  an  endless  screw  in  Fig.  5,  work- 
ing in  the  wheels  D  and  E,  whose  numbers  of  teeth 
being  equal,  and  should  be  equal  to  the  number  of 
lines  aS,  bS,  cS,  &c.  in  Fig.  4,  they  turn  round 
their  axes  in  equal  times  to  one  another,  and  to  the 
motion  of  the  elliptic  plates.  For  the  wheels  D  and 
E  having  an  equal  number  of  teeth,  the  plate  FF 
being  fixed  on  the  same  axis  with  the  wheel  E, 
and  the  plate  FF  turning  the  equally-large  plate 
GG,  by  a  cat- gut  string  round  them  both,  they 
must  all  go  round  their  axes  in  as  many  turns  of 
the  handle  A*  as  either  of  the  wheels  has  teeth. 

It  is  easy  to  see,  that  the  end  h  of  the  elliptical 
plate  FF  being  farther  from  its  axis  E  than  the 
opposite  end  i  is,  must  describe  a  circle  so  much 
the  larger  in  proportion;  and  must  therefore  move 
through  so  much  more  space  in  the  same  time;  and 
for  that  reason  the  end  //  moves  so  much  faster 
than  the  end  i,  although  it  goes  no  sooner  round 
the  centre  E.  But  then,  the  quick- moving  end  h 
of  the  plate  FF  leads  about  the  short  end  /z/f  of 
the  plate  GG  with  the  same  velocity ;  and  the  slow- 
moving  end  i  of  the  plate  FF  coming  half  round, 
as  to  B,  must  then  lead  the  long  end  k  of  the  plate 
GG  as  slowly  about.  So  that  the  elliptical  plate 
FF  and  it  axis  E  move  uniformly  and  equally 
quick  in  every  part  of  its  revolution ;  but  the 
elliptical  plate  GG,  together  with  its  axis  JT,  must 
move  very  unequally  in  different  parts  of  its  revo- 
lution ;  the  difference  being  always  inversely  as  the 
distance  of  any  points  of  the  circumference  of  GG 
from  its  axis  at  K:  or  in  other  words,  to  in- 
stance in  two  points ;  if  the  distance  Kk,  be  four, 
five,  or  six  times  as  great  as  the  distance  A7z,  the 
point  h  will  move  in  that  position  four,  five,  or  six 


The  improved  CELESTIAL  GLOBE  described.  447 

times  as  fast  as  the  point  k  does ;  when  the  plate 
GG  has  gone  half  round :  and  so  on  for  any  other 
eccentricity  or  difference  of  the  distances  Kk  and 
Kh.  The  tooth  i  on  the  plate  FF  falls  in  between 
the  two  teeth  at  k  on  the*  plate  GG,  by  which  means 
the  revolution  of  the  latter  is  so  adjusted  to  that 
of  the  former,  that  they  can  never  vary  from  one 
another. 

On  the  top  of  the  axis  of  the  equally-moving 
wheel  D,  in  Fig.  5th,  is  the  sun  S  in  Fig.  4th; 
which  sun,  by  the  wire  Z  fixed  to  it,  carries  the 
ball  1  round  the  circle  ABCD,  &c.  with  an  equa- 
ble motion  according  to  the  order  of  the  letters ; 
and  on  the  top  of  the  axis  JTof  the  unequally-mov- 
ing ellipsis  GG,  in  Fig.  5th,  is  the  sun  S  in  Fig. 
4th,  carrying  the  ball  Funequally  round  in  the  ellip- 
tical groove  abed,  &c.  JV".  B  This  elliptical  groove 
must  be  precisely  equal  and  similar  to  the  verge  of 
the  plate  GG,  which  is  also  equal  to  that  of  FF. 

In  this  manner,  machines  may  be  made  to  shew 
the  true  motion  of  the  Moon  about  the  Earth,  or  of 
any  planet  about  the  Sun ;  by  making  the  elliptical 
plates  of  the  same  eccentricities,  ia  proportion  to 
the  radius,  as  the  orbits  of  the  planets  are  whose 
motions  they  represent ;  and  so,, their  different  equa- 
tions, in  different  parts  of  their  orbits,  may  be  made 
plain  to  the  sight :  and'ciearer  ideas  of  these  motions 
and  equations  will  be  acquired  in  half  an  hour,  than 
could  be  gained  from  reading  half  a  day  about  them. 

401.  The  IMPROVED  CELESTIAL  GLOBE.  OnTheim- 
the  north  pole  of  the  axis,  above  the  hour-circle, 
is  fixed  an  arch  MKH tf  23*  degrees;  and  at  the 
end  //is  fixed  an  upright  pin  //G,  which  stands 
directly  over  the  north  pole  of  the  ecliptic,  and  per- 
pendicular to  that  part  of  the  surface  of  the  globe. 
On  this  pin  are  two  moveabie  collets  at  Z)  and  H^ 
to  which  are  fixed  the  quadrantal  wires  N  and  0,  Fi£- In- 

3L 


448  The  improved  CELESTIAL  GL QBE  described. 

having  two  little  balls  on  their  ends  for  the  sun  and 
moon,  as  in  the  figure.  The  collet  D  is  fixed  to 
the  circular  plate  F,  on  which  the  29i  days  of  the 
Moon's  age  are  engraven,  beginning  just  under  the 
sun's  wire  A";  and  as  this  ivire  is  moved  round  the 
globe,  the  plate  F  turns  round  with  it.  These  wires 
are  easily  turned,  if  the  screw  G  be  slackened ;  and 
when  they  are  set  to  their  proper  places,  the  screw 
serves  to  fix  them  there ;  so  that  when  the  globe  is 
turned,  the  wires  with  the  sun  and  moon  may  go 
round  with  it ;  and  these  two  little  balls  rise  and  set 
at  the  same  times,  and  on  the  same  points  of  the 
horizon,  for.ithe  day  to  which  they  are  rectified,  as 
the  Sun  and  Moon  do  in  the  heavens. 

Because  the  Moon  keeps  not  her  course,  in  the 
ecliptic  (as  the  Sun  appears  to  cio)  but  has  a  decli- 
nation of  5*.  degrees,  on  each  side,  from  it  in  every 
lunation,  §  317,  her  ball  may  be  screwed  as  many 
degrees  to  either  side  of  the  ecliptic  as  her  latitude, 
or  declination  from  the  ecliptic,  amounts  to,  at  any 
given  time ;  and  for  this  purpose  S  is  a  small  piece 
of  pasteboard,  of  which  the  curved  edge  at  S  is  to 
be  set  upon  the  globe,  at  right  angles  to  the  ecliptic, 
and  the  dark  line  over  S  to  stand  upright  upon  it. 
From  this  line,  on  the  convex  edge,  are  drawn  the 
5*  degrees  of  the  Moon's  latitude  on  both  sides  of 
the  ecliptic  ;  and  when  this  piece  is  set  upright  on 
the  globe,  its  graduated  edge  reaches  to  the  moon 
on  the  wire  0,  by  which  means  she  is  easily  adjust- 
ed to  her  latitude  found  by  an  ephemeris. 

The  horizon  is  supported  by  two  semicircular 
arches,  because  pillars  would  stop  the  progress  of 
the  balls,  when  they  go  below  the  horizon  in  an 
oblique  sphere. 

TO  rectify       To  rectify  this  globe.     Elevate  the  pole  to  the 
u*  latitude  of  the  place;  then  bring  the  Sun's  place 

in  the  ecliptic  for  the  given  clay  to  the  brass  meri- 
dian, and  set  the  hour-index  to  XII  at  noon,  that  is, 


The  PLANE T A R V  GLOBE  described. 

to  the  upper  XII  on  the  hour-circle,  keeping  the 
globe  in  that  situation ;  slacken  the  screw  G,  and 
set  the  sun  directly  over  his  place  on  the  meridian ; 
which  being  done,  set  the  moon's  wire  under  the 
number  that  expresses  her  age  for  that  day  on  the 
plate  F9  and  she  will  then  stand  over  her  place  in 
the  ecliptic,  and  shew  what  constellation  she  is  in. 
Lastly,  fasten  the  screw  G>  and  laying  the  curved 
edge  of  the  pasteboard  S  over  the  ecliptic,  below  the 
moon,  adjust  the  moon  to  her  latitude  over  the  gra- 
diuted  edge  of  the  pasteboard ;  and  the  globe  will 
be  rectified. 

Having  thus  rectified  the  globe*  turn  it  round,  and  its  ua>, 
observe  on  what  points  of  the  horizon  the  sun  and 
moon  balls  rise  and  set,  for  these  agree  with  the 
points  of  the  compass  on  which  the  Sun  and  Moon 
rise  and  set  in  the  heavens  on  the  given  day  :  and 
the  hour- index  shews  the  times  of  their  rising  and 
setting ;  and  likewise  the  time  of  the  Moon's  pass^ 
ing  over  t  he  meridian. 

This  simple  apparatus  shews  all  the  varieties  that 
can  happen  in  the  rising  and  setting  of  the  Sun  and 
Moon  ;  and  makes  the  ibrementioned  phenomena  of 
the  harvest- moon. (Chap,  xvi.)  plain  to  the  eye.  It 
is  also  very  useful  in  reading  lectures  on  the  globes, 
because  a  large  company  can  see  this  sun  and  moon 
go  round,  rising  above  and  setting  below  the  hori- 
zon at  different  times,  according  to  the  seasons  of 
the  year ;  and  making  their  appulses  to  different 
fixed  stars.  But  in  the  usual  way,  where  there  is 
only  the  places  of  the  Sun  and  Moon  in  the  ecliptic 
to  keep  the  eye  upon,  they  are  easily  lost  sight  of, 
.unless  they  be  covered  with  patches. 

402.  THE  PLANETARY  GLOBES.     In  this  ma- The 
chine,  TMs  a  terrestrial  globe  fixed  on  its  axis  stand-  *ETA* 
ing  upright  on  the  pedestal  CZXE,  on  which  is  anptate 
hour-circle,  having   its  index  fixed  on  the  axis,  V!IL 
which  turns  somewhat  tightly  in  the  pedestal,  soFlff>I> 


1  lie  PLANETARY  GLOBE  described, 

that  the  globe  may  not  be  liable  to  shake ;  to  prc* 
rent  which,  the  pedestal  is  about  two  inches  thick, 
and  the  axis  goes  quite  through  it,  bearing  on  a 
shoulder.  The  globe  is  hung  in  a  graduated  brazen 
meridian  much  in  the  usual  way ;  and  the  thin  plate 
JV,  NE\  E,  is  a  moveable  horizon,  graduated  round 
the  outer  edge,  for  shewing  the  bearings  and  ampli- 
tudes of  the  Sun,  Moon,  and  planets.    The  brazen 
meridian  is  grooved  round  the  outer  edge  :  and  in 
this  groove  is  a  slender  semicircle  of  brass,  the  ends 
of  which  are  fixed  to  the  horizon  in  its  north  and 
south  points:  this  semicircle  slides  in  the  groove 
as  the  horizon  is  moved  in  rectifying  it  for  different 
latitudes.    To  the  middle  of  the  semicircle  is  fixed 
a  pin,  which  always  keeps  in  the  zenith  of  the  hori- 
zon, and  on  this  pin,  the  quadrant  of  altitude  g  turns; 
the  lower  end  of  which,  in  ail  positions,  touches  the 
horizon  as  it  is  moved  round  the  same.  This  quad- 
rant is  divided  into  90  degrees  from  the  horizon  to 
the  zenith-pin  on  which  it  is  turned,  at  PO.     The 
great  flat  circle  or  plate  AE  is  the  ecliptic,  on  the 
outer  edge  of  which  the  signs  and  degrees  are  laid 
down ;  and  every  fifth  degree  is  drawn  through  the 
rest  of  the  surface  of  this  plate  toward  its  centre. 
On  this  plate  are  seven  grooves,  to  which  seven  little 
balls  are  adjusted  by  sliding  wires,  so  that  they  are 
easily  moved  in  the  grooves  without  danger  of  start- 
ing  out  of  them.  The  ball  next  the  terrestrial  globe 
is  the  moon,  the  next  without  it  is  Mercury,  the 
next  Venus,  the  next  the  sun,  then  Mars,  then  Jupi- 
ter, and  lastly  Saturn ;  and  in  order  to  know  them, 
they  are  separately  stampt  with  the  following  charac- 
ters; •  ,$,  9,0,£,V,i2.    This  plate  or  eclip- 
tic is  supported  by  four  strong  wires,  having' their 
lower  ends  fixed  into  the  pedestal,  at  6T,  />,  and  E; 
the  fourth  being  hid  by  the  globe.     The  ecliptic  is 
inclined  23*  degrees  to  the  pedestal,  and  is  there- 


The  PLANETARY  GLOBE  described.  45 1 

fore  properly  inclined  to  the  axis  of  the  globe  which 
stands  upright  on  the  pedestal. 

To  rectify  this  machine.  Set  the  sun  and  all  the 
planetary  balls  to  the  geocentric  places  in  the  eclip- 
tic for  any  given  time,  by  an  ephemcris ;  then  set 
the  north  point  of  the  horizon  to  the  latitude  of  your 
place  on  the  brazen  meridian,  and  the  quadrant  of 
altitude  to  the  south  point  of  the  horizon ;  which 
done,  turn  the  globe  with  its  furniture  till  the  quad* 
rant  of  altitude  comes  right  against  the  Sun,  viz.  to 
his  place  in  the  ecliptic ;  and  keeping  it  there,  set 
the  hour-index  to  the  XII  next  the  letter  C;  and 
the  machine  will  be  rectified,  not  only  for  the  follow- 
ing problems,  but  for  several  others,  which  the  art- 
ist may  easily  find  out. 

*  V 

PROBLEM  I. 

To  find  the  Amplitudes,  Meridian* Altitudes ',  and 
Tunes  of  rising^  culminating,  and  setting^  oftlie 
Sun,  Moony  and  Planets. 

\ 

Turn  the  globe  round  eastward,  or  according  to  its  use, 
the  order  of  the  signs ;  and  when  the  eastern  edge  of 
the  horizon  comes  right  against  the  sun,  moon,  or 
any  planet,  the  hour-index  will  shew  the  time  of  its 
rising ;  and  the  inner  edge  of  the  ecliptic  will  cut  its 
rising-amplitude  in  the  horizon.  Turn  on,  and  when 
the  quadrant  of  altitude  comes  right  against  the  sun, 
moon,  or  any  planet,  the  ecliptic  will  cut  their  meri- 
dian-altitudes on  the  quadrant,  and  the  hour-index 
will  shew  the  times  of  their  coming  to  the  meridian. 
Continue  turning,  and  when  the  western  edge  of  the 
horizon  comes  right  against  the  sun,  moon,  or  any 
planet,  their  setting-amplitudes  will  be  cut  on  the 
horizon  by  the  ecliptic  ;  and  the  times  of  their  set- 
ting will  be  shewn  by  the  index  en  the  hour-circle. 


452  The  PLANETARY  GL o u E  described. 


PROBLEM  II. 

To  find  the  Altitude  and  Azimuth  of  the  Sun, 

and  Planets,  at  any  Time  of  their  being  above 
the  Horizon. 

Turn  the  globe  till  the  index  comes  to  the  given 
time  in  the  hour-circle ;  then  keep  the  globe  steady; 
and  moving  the  quadrant  of  altitude  to  each  planet 
respectively,  the  edge  of  the  ecliptic  will  cut  the 
planet's  mean  altitude  on  the  quadrant,  and  the 
quadrant  will  cut  the  planet's  azimuth,  or  point  of 
bearing  on  the  horizon. 


PROBLEM  III. 

The  Sun's  Altitude  being  given  at  any  Time  either 
before  or  after  Noon,  to  find  the  Hour  of  the  Day, 
and  the  Variation  of  the  Compass,  in  any  known 
Latitude. 

With  one  hand  hold  the  edge  of  the  quadrant 
right  against  the  sun ;  and  with  the  other  hand,  turn 
the  globe  westward,  if  it  be  in  the  forenoon,  or  east- 
ward if  it  be  in  the  afternoon,  until  the  sun's  place 
at  the  inner  edge  of  the  ecliptic  cuts  the  quadrant  in 
the  sun's  observed  altitude,  and  then  the  hour-index 
will  point  out  the  time  of  the  day,  and  the  quadrant 
will  cut  the  true  azimuth  or  bearing  of  the  sun  for 
that  time :  the  difference  between  which,  and  the 
bearing  shewn  by  the  azimuth-compass,  is  the  vari- 
ation of  the  compass  in  that  place  of  the  Earth. 
The  TRA-  403.  THE  TR AJECTORIUM  LUN ARE.  Thisma- 
c^ne  *s  *°r  delineating  the  paths  of  the  Earth  and 
Moon,  shewing  what  sort  of  curves  they  make  in 
the  ethereal  regions ;  and  was  just  mentioned  in 


The  TRAJECTORIUM  LUNARE  described.  453 


PLATE 
VII. 


the  266th  article.  S  is  the  sun,  and  E  the  earth, 
whose  centres  are  8 1  inches  distant  from  each  other ; 
every  inch  answering  to  a  million  of  miles,  J  47. 
M  is  the  moon,  whose  centre  is  ^  parts  of  an  inch 
from  the  earth's  in  this  machine,  this  being  in  just 
proportion  to  the  Moon's  distance  from  the  Earth, 
$52.  A  A  is  a  bar  of  wood,  to  be  moved  by  hand 
round  the  axis  g,  which  is  fixed  in  the  wheel  y. 
The  circumference  of  this  wheel  is  to  the  circum- 
ference of  the  small  wheel  L  (below  the  other  end 
of  the  bar)  as  365 J  days  is  to  29|;  or  as  a  year  is  to 
a  lunation.  The  wheels  are  grooved  round  their 
edges,  and  in  the  grooves  is  the  cat-gut  string  GG 
crossing  between  the  wheels  at  X.  On  the  axis  of 
the  wheel  L  is  the  index  F ;  in  which  is  fixed  the 
moon's  axis  M  for  carrying  her  round  the  earth  E 
(fixed  on  the  axis  of  the  wheel  L)  in  the  time  that 
the  index  goes  round  a  circle  of  29-J  equal  parts, 
which  are  the  days  of  the  Moon's  age.  The  wheel 
Y  has  the  months  and  days  of  the  year  all  round  its 
limb ;  and  in  the  bar  AA  is  fixed  the  index  /,  which 
points  out  the  days  of  the  months  answering  to  the 
days  of  the  moon's  age  shewn  by  the  index  F>  in 
the  circle  of  29  J  equal  parts,  at  the  other  end  of  the 
bar.  On  the  axis  of  the  wheel  L  is  put  the  piece  , 
D  below  the  cock  C,  in  which  this  axis  turns  round ; 
and  in  D  are  put  the  pencils  e  and  772,  directly  under 
the  earth  E  and  moon  M;  so  that  m  is  carried 
round  e,  as  Mis  round  E. 

Lay  the  machine  on  an  even  fioor,  pressing  Its  usc 
gently  on  the  wheel  F,  to  cause  its  spiked  feet  (of 
which  two  appear  at  P  and  P,  the  third  being  sup- 
posed  to  be  hid  from  sight  by  the  wheel)  to  enter  a 
little  into  the  floor  to  secure  the  wheel  from  turning. 
Then  lay  a  paper  about  four  feet  long  under  the 
pencils  e.  and  m,  cross- wise  to  the  bar :  which  done 
move  the  bar  slowly  round  the  axis  g  of  the  wheel 
Y;  and,  as  the  earth  E  goes  round  the  sun  S,  the 
Jioon  M  will  go  round  the  earth  with  a  duly  pro* 


454  The  TIDE-DIAL  described. 

portioned  velocity;  and  the  friction- wheel 
ning  on  the  floor,  will  keep  the  bar  from  bearing 
too  heavily  on  the  pencils  e  and  772,  which  will  de- 
lineate the  paths  of  the  earth  and  moon,  as  in  Fig. 
2d,  already  described  at  large,  §  266,  267.  As  the 
index  /  points  out  the  days  of  the  months,  the  in- 
dex  jF  shews  the  Moon's  age  on  these  days  in  the 
circle  of  29£  equal  parts.  And  as  this  last  index 
points  to  the  different  days  in  its  circle,  the  like 
numeral  figures  may  be  set  to  those  parts  of  the 
curves  of  the  earth's  path  and  moon's,  where  the 
pencils  e  and  m  are  at  those  times  respectively,  to 
shew  the  places  of  the  earth  and  moon.  If  the  pen- 
cil c  be  pushed  a  very  little  oif,  as  if  from  the  pencil 
my  to  about  —•  part  of  their  distance,  and  the  pencil 
772  pushed  as  much  toward  e  to  bring  them  to  the 
same  distance  again,  though  not  to  the  same  points 
of  space ;  then  as  m  goes  round  e,  e  will  go  as  it 
were  round  the  centre  of  gravity  between  the  earth 
€  and  moon  m,  §  298 :  but  this  motion  will  not 
sensibly  alter  the  figure  of  the  earth's  path  or  the 
moon's. 

If  a  pin,  as/>,  be  put  through  the  pencil  777,  with 
its  head  toward  that  of  the  pin  q  in  the  pencil  e,  the 
'  head  of  the  former  will  always  keep  to  the  head  of 
the  latter  as  m  goes  round  c,  and  shews  that  the 
same  side  of  the  Moon  is  continually  turned  to  the 
Earth.  But  the  pin/?,  which  may  be  considered  as 
an  equatprial  diameter  of  the  moon  will  turn  quite 
round  the  point  772,  making  all  possible  angles  v.ith 
the  line  of  its  progress,  or  line  of  the  moon's  path. 
This  is  an  ocular  proof  of  the  Moon's  turning  round 
her  axis. 

TheTiDE-     404.   The  TIDE-DIAL.     The  outside  parts  of 

DIAL.      tnis  machine  consist  of,  1.  An  eight-sided  box,  on 

Fig!Vii.  *ne  top,  of  which  at  the  corners  is  shewn  the  phases 

of  the  Moon  at   the   octants,  quarters,  and  full. 

Within  these  is  a  circle  of  29|  equal  parts,  which 

,     are  the  days  of  the  Moon's  age  accounted  from  the 

Sun  at  new  Moon,  round  to  the  Sun  again.  Within 


The  TIDE-DIAL  described.  455 

this  circle  is  one  of  24  hours  divided  into  their  re- 
spective halves  and  quarters.  2.  A  moving  ellipti- 
cal plate,  painted  blue,  to  represent  the  rising  of 
the  tides  under  and  opposite  to  the  Moon ;  and  hav- 
ing the  words,  Hndi  Water,  Tide  Falling,  Low 
Water,  Tide  Rising,  marked  upon  it.  To  one 
end  of  this  plate  is  fixed  the  moon  M,  by  the  wire 
W,  and  goes  along  with  it.  3.  Above  this  ellipti- 
cal plate  is  a  round  one,  with  the  points  of  the  com- 
pass upon  it,  and  also  the  names  of  above  200  places 
in  the  large  machine  (but  only  32  in  the  figure,  to 
avoid  confusion)  set  over  those  points  on  which  the 
Moon  bears  when  she  raises  the  tides  to  the  great- 
est heights,  at  these  places,  twice  in  every  lunar  day : 
and  to  the  north  and  south  points  .of  this  plate  are 
fixed  two  indexes,  /  and  K,  which  shew  the  times 
of  high  water,  in  the  hour-circle,  at  all  these  places. 
4.  Below  the  elliptical  plate  are  four  small  plates, 
two  of  which  project  out  from  below  its  ends  at 
new  and  full  Moon ;  and  so,  by  lengthening  the 
ellipse,  shew  the  spring-tides,  which  are  then  raised 
to  the  greatest  heights  by  the  united  attractions  of 
the  Sun  and  Moon,  $  302.  The  other  two  of  these  its  use. 
small  plates  appear  at  low  water  when  the  Moon  is 
in  her  quadratures,  or  at  the  sides  of  the  elliptical 
plate  to  shew  the  neap-tides ;  the  Sun  and  Moon 
then  acting  cross-wise  to  each  other.  When  any 
two  of  these  small  plates  appear,  the  other  two  are 
hid  ;  and  when  the  Moon  is  in  her  octants,  they  all 
disappear,  there  being  neither  spring  nor  neap- 
tides  at  those  times.  Within  the  box  are  a  few 
wheels  for  performing  these  motions  by  the  handle 
or  winch  H. 

Turn  the  handle  until  the  moon  M  comes  to 
any  given  day  of  her  age  in  the  circle  of  is9|  equal 
parts,  and  the  moon's  wire  W,  will  cut  the  time 
of  ter  coming  to  the  meridian  on  that  day,  in  the 
hour  circle ;  the  XII  under  the  sun  being  mid-day, 
and  the  opposite  XII  midnight ;  then  looking  for 
the  name  of  any  given  place  on  the  round  plate 

3  M 


456  The  TIDE-DIAL  described. 

(which  makes  29|  rotations  while  the  moon  M 
makes  only  one  revolution  from  the  sun  to  the  sun 
again)  turn  the  handle  till  that  place  comes  to  the 
word  High  Water  under  the  moon,  and  the  index 
which  falls  among  the  forenoc  i- hours  will  shew  the 
time  of  high  water  at  that  place  in  the  forenoon  of 
the  given  day :  then  turn  the  plate  half  round,  till 
the  same  place  comes  to  the  opposite  high-water- 
mark, and  the  index  will  shew  the  lime  of  high 
water  in  the  afternoon  at  that  place.     And  thus,  as 
all  the  different  places  come  successively  under  and 
opposite  to  the  moon,  the  indexes  shew  the  times 
of  high  water  at  them  in  both  parts  of  the  day  :  and 
when  the  same  places  come  to  the  low- water-marks, 
the  indexes  shew  the  times  of  low  water.  For  about 
three  days  before  and  after  the  times  of  new  and  full 
Moon,  the  two  small  plates  come  out  a  little  way 
from  below  the  high-water-marks  on  the  elliptical 
plate,  to  shew  that  the  tides  rise  still  higher  about 
these  times :  and  about  the  quarters,  the  other  two 
plates  come  out  a  little  from  under  the  low-water- 
marks toward  the  sun  and  on  the  opposite  side, 
shewing  that  the  tides  of  flood  rise  not  then  so 
high,  nor  do  the  tides  of  ebb  fall  so  low,  as  at  other 
times. 

By  pulling  the  handle  a  little  way  outward,  it 
is  disengaged  from  the  wheel  work,  and  then  the 
upper  plate  may  be  turned  round  quickly  by  hand, 
so  that  the  moon  may  thus  be  brought  to  any  given 
day  of  her  age  in  about  a  quarter  of  a  minute  :  and 
by  pushing  in  the  handle,  it  takes  hold  of  the  wheel- 
work  again. 

The  inside     On  «3^»  tne  ax*s  °f  t^ie  handle  //,  is  an  endless 

work  de-   screw  C,  which  turns  the  wheel  FED  of  24  teeth 

scribed.     roun(j  jn  24  revolutions  of  the  handle  :  this  wheel 

turns  another  ONG,  of  48  teeth,  and  on  its  axis 

Plate  ix.  is  the  pinion  jPQ  of  four  leaves,  which  turns  the 

Tig.  VIH.  wheel  LKI  of  59  teeth  round  in  29^  turnings  or 

rotations  of  the  wheel  FED,  or  in  7U8  revolu- 


The  DIAL-PLATE  described.  457 

tions  of  the  handle,  which  is  the  number  of  hours 
in  a  synodical  revolution  of  the  Moon.  The  round 
plate  with  the  names  of  places  upon  it  is  fixed  on 
the  axis  of  the  wheel  FED ;  and  the  elliptical  or 
tide-plate  with  the  moon  fixed  to  it  is  upon  the  axis 
of  the  wheel  LK1 ' ;  consequently,  the  former  makes 
29£  revolutions  in  the  time  that  the  latter  makes 
one.  The  whole  wheel  FED*  with  the  endless 
screw  C,  and  dotted  part  of  the  axis  of  the  handle 
AB)  together  with  the  dotted  part  of  the  wheel 
OA'G,  lie  hid  below  the  large  wheel  LKI. 

Fig.  IXth  represents  the  under  side  of  the  ellip- 
tical or  tide-plate  ahcd,  with  the  four  small  plates 
ABCD,  EFGH,  IKLM,  JVOPQ  upon  it :  each 
of  which  has  two  slits,  as  7T,  SS,  RR,  UU,  slid- 
ing on  two  pins,  as  nn,  fixed  in  the  elliptical  platef 
In  the  four  small  plates  are  fixed  four  pins,  at  7F", 
X,  F,  and  Z;  all  of  which  work  in  an  elliptic  groove 
oooo  on  the  cover  of  the  box  below  the  elliptical 
plate  ;  the  longest  axis  of  this  groove  being  in  a  right 
line  with  the  sun  and  full  moon.  Consequently, 
when  the  moon  is  in  conjunction  or  opposition, 
the  pins  /Fand  X thrust  out  the  plates  ABCD  and 
IKLM  a.  little  beyond  the  ends  of  the  elliptical  plate 
at  d  and  6,  to  f  and  e  ;  while  the  pins  F  and  Z 
draw  in  the  plates  EFGHand  NOPQ  quite  under 
the  elliptic  plate  to  g  and  h.  But,  when  the  moon 
comes  to  her  first  or  third  quarter,  the  elliptic  plate 
lies  across  the  fixed  elliptic  groove  in  which  the 
pins  work;  and  therefore  the  end- plates  ABCD 
and  IKLMwcz  drawn  in  below  the  great  plate,  and 
the  other  two  plates  EFGH.and  NOPQ  are  thrust 
out  beyond  it  to  a  and  c.  When  the  moon  is  in 
her  octants,  the  pins  T7,  X,  F,  Z  are  in  the  parts 
o,  o,  0,  o  of  the  elliptic  groove,  which  parts  are  at  3 
mean  between  the  greatest  and  least  distances  from 
the  centre  ^,  and  then  all  the  four  small  plates  dis,r 
appear,  being  hid  by  the  great  one, 


458  The  ECLIPSAREON  described. 

The  405.  The  ECLIPSAREON.     This  piece  of  me- 

Kilo"8*"  chan*sm  exhibits  the  time,  quantity,  duration,  and 
Plate'  progress  of  solar  eclipses,  at  all  parts  of  the  Earth. 
X.UL  rfhe  principal  parts  of  this  machine  are,  1.  A 

terrestrial  globe  A,  turned  round  its  axis  J3y  by  the 
handle  or  winch  M;  the  axis  B  inclines  23^  de- 
grees, and  has  an  index  which  goes  round  the 
hour-circle  D  in  each  rotation  of  the  globe.  2. 
A  circular  plate  jE,  on  the  limb  of  which  the 
months  and  days  of  the  year  are  inserted.  This 
plate  supports  the  globe,  and  gives  its  axis  the 
same  position  to  the  Sun,  or  to  a  candle  properly 
placed,  that  the  Earth's  axis  has  to  the  Sun  upon 
any  day  of  the  year,  §  338,  by  turning  the  plate 
till  the  given  day  of  the  month  comes  to  the  fixed 
pointer,  or  annual  index  G.  3.  A  crooked  wire 
F,  which  points  toward  the  middle  of  the  Earth's 
enlightened  disc  at  all  times,  and  shews  to  what 
place  of  the  Earth  the  Sun  is  vertical  at  any  given 
time.  4.  A  penumbra,  or  thin  circular  plate  of 
brass  /,  divided  into  12  digits  by  12  concentric 
circles,  which  represent  a  section  of  the  Moon's 
penumbra,  and  is  proportioned  to  the  size  of  the 
globe  ;  so  that  the  shadow  of  this  plate,  formed  by 
the  Sun  or  a  candle  placed  at  a  convenient  distance, 
with  its  rays  transmitted  through  a  convex  lens  to 
make  them  fall  parallel  on  the  globe,  covers  exactly 
all  those  places  upon  it  that  the  Moon's  shadow 
and  penumbra  do  on  the  Earth  ;  so  that  the  phen- 
umena  of  any  solar  eclipse  may  be  shewn  by  this 
machine  with  candle-light  almost  as  well  as  by  the 
light  of  the  Sun.  5.  An  upright  frame  HHHHy 
on  the  sides  of  which  are  scales  of  the  Moon's  lati- 
tude or  declination  from  the  ecliptic.  To  these 
scales  are  fitted  two  sliders  A"  and  K,  with  indexes 
for  adjusting  the  penumbra's  centre  to  the  Moon's 
latitude,  as  it  is  north  or  south  ascending  or  de- 
scending. 6,  A  solar  horizon  C,  dividing  the 


The  ECLIPSAREON  described.  459 

enlightened  hemisphere  of  the  globe  from  that 
which  is  in  the  dark  at  any  given  time,  and  shew- 
ing at  what  places  the  general  eclipse  begins  and 
eiids  with  the  rising  or  setting  Sun.  7.  A  handle 
M,  which  turns  the  globe  round  its  axis  by  wheel- 
work,  and  at  the  same  time  moves  the  penumbra 
across  the  frame  by  threads  over  the  pulleys  Z/,  Z/,  L, 
with  a  velocity  duly  proportioned  to  that  of  the 
Moon's  shadow  over  the  Earth,  as  the  earth  turns 
on  its  axis.  And  as  the  Moon's  motion  is  quicker 
or  slower  according  to  her  different  distances  from 
the  Earth,  the  penumbral  motion  is  easily  regulated 
in  the  machine  by  changing  one  of  the  pulleys. 

To  rectify  the  machine  for  use.  The  true  time  TO  rectify 
of  new  Moon  and  her  latitude  being  known  by  the Jt< 
foregoing  precepts,  §  353,  et  seq.  if  her  latitude 
exceed  the  number  of  minutes  or  divisions  on  the 
scales  (which  are  on  the  side  of  the  frame  hid  from 
view  in  the  figure  of  the  machine)  there  can  be  no 
eclipse  of  the  Sun  at  that  conjunction ;  but  if  it  do 
not,  the  Sun  will  be  eclipsed  to  some  places  of  the 
Earth ;  and,  to  shew  the  times  and  various  appear- 
ances  of  the  eclipse  at  those  places,  proceed  in  order 
as  follows. 

To  rectify  the  machine  for  performing  by  the 
light  of  the  Sun.  1.  Move  the  sliders  ZiT,  K,  till  their 
indexes  point  to  the  Moon's  latitude  on  the  scales, 
as  it  is  north  or  south  ascending  or  descending,  at 
that  time.  2.  Turn  the  month-plate  E  till  the  day 
of  the  given  new  Moon  comes  to  the  annual  index 
G.  3 .  "Unscrew  the  collar  JV  a  little  on  the  axis  of 
the  handle,  to  loosen  the  contiguous  socket  on  ^ 
which  the  threads  that  move  the  penumbra  are 
wound,  and  set  the  penumbra  by  hand  till  its 
centre  comes  to  the  perpendicular  thread  in  the 
middle  of  the  frame ;  which  thread  represents  the 
axis  of  the  ecliptic.  4.  Turn  the  handle  till  the 
meridian  of  London  on  the  globe  comes  just  under 
the  point  of  the  crooked  wire  F;  then  stop,  and 
turn  the  hour-circle  D  by  hand  till  XII  at  nooit 


460  The  ECLIPSAREON  described. 

Comes  to  its  index,  and  set  the  penumbra's  middle 
to  the  thread.  5.  Turn  the  handle  till  the  hour- 
index  points  to  the  time  of  new  Moon  in  the  circle 
I) ;  and  holding  it  there,  screw  last  the  collar  A* 
Lastly,  elevate  the  machine  till  the  Sun  shines 
through  the  sight-holes  in  the  small  upright  plates 
O,  O,  on  the  pedestal ;  and  the  whole  machine  will 
be  rectified. 

To  rectify  the  machine  for  shewing  by  candle- 
light. Proceed  in  every  respect  as  above,  except  in 
that  part  of  the  last  paragraph  where  the  Sun  is  men- 
tioned ;  instead  of  which,  place  a  candle  before  the 
machine,  about  four  yards  from  it,  so  that  the 
shadow  of  intersection  of  the  cross  threads  in  the 
middle  of  the  frame  may  fall  precisely  on  that  part 
of  the  globe  to  which  the  crooked  wire  F  points ; 
then,  with  a  pair  of  compasses,  take  the  distance 
between  the  penumbra's  centre  and  intersection  of 
the  threads ;  and  cqiuil  to  that  distance  set  the  can- 
dle higher  or  lower,  as  the  penumbra's  centre  is 
above  or  below  the  said  intersection.  Lastly,  place 
a  large  convex  lens  between  the  machine  and  candle, 
so  as  that  the  candle  may  be  ir.  the  focus  of  the  lens, 
and  then  the  rays  will  fall  parallel,  and  cast  a  strong 
light  on  the  globe. 

Its  use.  These  things  being  done,  (and  they  may  be  done 
sooner  than  they  can  be  expressed)  turn  the  handle 
backward,  until  the  penumbra  almost  touches  the 
side  HF  of  the  frame  ;  then  turning  gradually  for- 
ward, observe  the  following  phenomena.  1.  Where 
the  eastern  edge  of  the  shadow  of  the  penurnbral 
plate  /  first  touches  the  globe  at  the  solar  horizon : 
those  who  inhabit  the  corresponding  part  of  the 
Earth  see  the  eclipse  begin  on  the  uppermost  edge 
of  the  Sun,  just  at  the  time  of  its  rising.  2.  In  that 
place  where  the  penumbra's  centre  first  touches  the 
globe,  the  inhabitants  have  the  Sun  rising  upon 
them  centrally  eclipsed,  3.  When  the  whole  penum- 
bra just  falls  upon  the  globe,  its  western  edge  at  the 
solar  horizon  touches"  and  leaves  the  place  where 


The  ECLIPSAREON  described.  461 

the  eclipse  ends  at  Sun -rise  on  the  lowermost  edge. 
Continue  turning ;  and,  4.  the  cross  lines  in  the 
centre  of  the  penumbra  will  go  over  all  those  places 
on  the  globe  where  the  Sun  is  centrally  eclipsed.  5. 
When  the  eastern  edge  of  the  shadow  touches  any 
place  of  the  globe,  the  eclipse  begins  there  ;  when 
the  vertical  line  in  the  penumbra  comes  to  any  place, 
then  is  the  greatest  obscuration  at  that  place ;  and 
when  the  western  edge  of  the  penumbra  leaves  the 
place,  the  eclipse  ends  there  ;  the  times  of  all  which 
are  shewn  on  the  hour-circle ;  and  from  the  begin- 
ning to  the  end,  the  shadows  of  the  concentric  pe- 
numbral  circles  shew  the  number  of  digits  eclipsed 
at  all  the  intermediate  times.    6.  When  the  eastern 
edge  of  the  penumbra  leaves  the  globe  at  the  solar 
horizon  C,  the  inhabitants  see  the  Sun  beginning  to 
be  eclipsed  on  his  lowermost  edge  at  its  setting. 
7.  Where  the  penumbra's  centre  leaves  the  globe, 
the  inhabitants  see  the  Sun  set  centrally  eclipsed. 
And  lastly,  where  the  penumbra  is  wholly  depart- 
ing from  the  globe,  the  inhabitants  see  the  eclipse 
ending  on  the  uppermost  part  of  the  Sun's  edge,  at 
the  time  of  its  disappearing  in  the  horizon. 

A".  B.  If  any  given  day  of  the  year  on  the  plate 
E  be  set  to  the  annual-index  6r,  and  the  handle 
turned  till  the  meridian  of  any  place  comes  under 
the  point  of  the  crooked  wire,  and  then  the  hour- 
circle  D  set  by  the  hand  till  XII  comes  to  its 
index ;  in  turning  the  globe  round  by  the  handle, 
when  the  said  place  touches  the  eastern  edge  of 
the  hoop  or  solar  horizon  C,  the  index  shews  the 
time  of  Sun- setting  at  that  place ;  and  when  the 
place  is  just  coming  out  from  below  the  other  edge 
of  the  hoop  C,  the  index  shews  the  time  when 
the  evening-twilight  'ends  to  it.  When  the  place 
has  gone  through  the  dark  part  A,  and  comes  abcut 
so  as  to  touch  under  the  back  of  the  hoop  C>  on 


462  7 7ze  E c  L  i  rs A R  E  o  N  described. 

the  other  side,  the  index  shews  the  time  when  the 
morning- twilight  begins ;  and  when  the  same  place 
is  just  coming  out  from  below  the  edge  of  the  hoop 
next  the  frame,  the  index  points  out  the  time  of 
Sun-rising.  And  thus,  the  times  of  the  Sun's  ris- 
sing  and  setting  are  shewn  at  all  places  in  one  rota- 
tion of  the  globe,  for  any  given  day  of  the  year :  and 
the  point  oi' the  crooked  wire  F  shews  all  the  places 
over  which  the  Sun  passes  vertically  on  that  day. 


A  PLAIN  METHOD 


OF    FINDING    THE 


DISTANCES  OF  ALL  THE  PLANETS 
FROM  THE  SUN, 


BY    THE 

TRANSIT  OF  VENUS  OVER  THE  SUN's 
DISC,  IN  THE  YEAR  1761. 

TO  WHICH  IS  SUBJOINED, 

AN  ACCOUNT  OF  MR.  HORROX's  OBSERVATIONS 

OF  THE  TRANSIT  OF  VENUS  IN 

THE  YEAR  1639: 

AND  ALSO, 

«F  THE  DISTANCES  OF  ALL  THE  PLANETS  FROM  THE 

SUN,  AS  DEDUCED  FROM  OBSERVATIONS  OF 

THE  TRANSIT  IN  THE  YEAR  17M. 


3N 


THE  METHOD 

O»    FINDING 

THE  DISTANCES  OF  THE  PLANETS 

FROM  THE  SUN. 


CHAPTER  XXIIL 

ARTICLE  I. 

Concerning  parallaxes,  and  their  use  in  general. 

r  |^  HE*  approaching  transit  of  Venus  over  the 
jL  Sun  has  justly  engaged  the  attention  of  as- 
tronomers, as  it  is  a  phenomenon  seldom  seen,  and 
as  the  parallaxes  of  the  Sun  and  planets,  and  their 
distances  from  one  another,  may  be  found  with 
greater  accuracy  by  it,  than  by  any  other  method 
yet  known. 

2.  The  parallax  of  the  Sun,  Moon,  or  any  planet, 
is  the  distance  between  its  true  and  apparent  place 
in  the  heavens.  The  true  place  of  any  celestial  ob- 
ject, referred  to  the  starry  heaven,  is  that  in  which 
it  would  appear  if  seen  from  the  centre  of  the  Earth; 
the  apparent  place  is  that  in  which  it  appears  as  seen 
from  the  Earth's  surface. 

To  explain  this,  let  AJBDHbe  the  Earth  (Fig.  T. 
of  Plate  XiV.)>  C  its  centre,  M  the  Moon,  and 
Z.XR  an  arc  of  the  starry  heaven.  To  an  observer 
at  C  (supposing  the  Earth  to  be  transparent)  the 
Moon  M  will  appear  at  £7,  which  is  her  true  place, 

*  The  whole  of  this  Dissertation  Was  published  in  the  beginning 
of  th'.»  year  1761,  before  the  time   :f  the  transit,  except  the  7th 
8th  articles,  which  are  added  since  that  time. 


466  Tlic  Method  of  folding  the  Distances 

referred  to  the  starry  firmament :  but  at  the  same 
instant,  to  an  observer  at  A,  she  will  appear  at  Uj 
below  her  true  place  among  the  stars. — The  angle 
AMC  is  called  the  Moon's  parallax,  and  is  equal  to 
the  opposite  angle  UMu9  whose  measure  is  the 
celestial  arc  Uu. — The  whole  earth  is  but  a  point  if 
compared  with  its  distance  from  the  fixed  stars,  and 
therefore  we  consider  the  stars  as  having  no  paral- 
lax at  all. 

3.  The  nearer  the  object  is  to  the  horizon,  the 
greater  is  its  parallax  ;  the  nearer  it  is  to  the  zenith, 
the  less.    In  the  horizon  it  is  greatest  of  all ;  in  the 
zenith  it  is  nothing. — Thus  \z\.AL,t  be  the  sensible 
horizon  of  an  observer  at  A  ;  to  him  the  Moon  at 
L  is  in  the  horizon,  and  her  parallax  is  the  angle 
ALC,  under  which  the  Earth's  semidiameter  AC 
appears  as  seen  from  her.     This  angle  is  called  the 
Moon's  horizontal  parallax,  and  is  equal  to  the  op- 
posite angle  TLt9  whose  measure  is  the  arc  Tt  in 
the  starry  heaven.     As  the  Moon  rises  higher  and 
higher  to  the  points  M,  A",  0,  P,  in  her  diurnal 
course,  the  parallactic  angles   UMu,  XNx,    Toy 
diminish,  and  so  do  the  arcs  Uu,  Xx,  Yy,  which 
are  their  measures,  until  the  Moon  comes  to  P*j 
and  then  she  appears  in  the  zenith  Z  without  any 
parallax,  her  place  being  the  same  whether  it  be  seen 
from  A  on  the  Earth's  surface,  or  from  Cits  centre, 

4.  If  the  observer  at  A  could  take  the  true  mea- 
sure or  quantity  of  the  paraliactic  angle  ALC,  he 
might  by  that  means  find  the  Moon's  distance  from 
the  centre  of  the  Earth.     For,  in  the  plane  tri- 
angle LACr  the  side  AC,   which  is  the  Earth's 
semidiameter,  the  angle  ALC,  which  is  the  Moon's 
horizontal    parallax,    and  the   right   angle    CALy 
•would  be  given.     Therefore,  by  trigonometry,  as 
the  tangent  of  the  parallactic  angle  ALC  is  to  ra- 
dius, so  is  the  Earth's  semidiameter  AC  to  the 
Moon's  distance  CL  from  the  Earth's  centre  CV — 
But  because  we  consider  the  Earth's  semidiameter 
as  unity,  and  the  logarithm  of  unity  is  nothing,  sub* 


of  the  Planets  from  the  Sun.  467 

tract  the  logarithmic  tangent  of  the  angle  ALC 
from  radius,  and  the  remainder  will  be  the  logarithm 
of  CX,  and  its  c  responding  number  is  the  num- 
ber of  semi- diameters  of  the  Earth  which  the  Moon 
is  distant  from  the  Earth's  centre. — Thus,  suppos- 
ing the  angle  ALC  of  the  Moon's  horizontal  paral- 
lax to  be  57'  18", 

From  the  radius  10.0000000 

Subtract  the  tangent  of  57'  18"        8.2219207 


And  there  will  remain  —          1.7780793 

which  is  the  logarithm  of  59.99,  the  number  of  semi- 
diameters  of  the  Earth  which  are  equal  to  the  Moon's 
distance  from  the  Earth's  centre.  Then,  59.99  be- 
ing multiplied  by  3985,  the  number  of  miles  con- 
tained in  the  Earth's  semidiameter,  will  give  239060 
miles  for  the  Moon's  distance  from  the  centre  of  the 
Earth,  by  this  parallax. 

5.  But  the  true  quantity  of  the  Moon's  horizon- 
tal parallax  cannot  be  accurately  determined  by  ob- 
serving the  Moon  in  the  horizon,  on  account  of  the 
inconstancy  of  the  horizontal  refractions,  which  al- 
ways vary  according  to  the  state  of  the  atmosphere; 
and  at  a  mean  rate,  elevate  the  Moon's  apparent 
place  near  the  horizon  half  as  much  as  her  parallax 
depresses  it.  And  therefore  to  have  her  par- 
allax more  accurate,  astronomers  have  thought  of 
the  following  method,  which  seems  to  be  a  very 
good  one,  but  hath  not  yet  been  put  in  practice. 

Let  two  observers  be  placed  under  the  same  me- 
ridian, one  in  the  northern  hemisphere,  and  the 
other  in  the  southern,  at  such  a  distance  from  each 
other,  that  the  arc  of  the  celestial  meridian  inclu<  d 
between  their  two  zeniths  may  be  at  least  80  or  90 
degrees.  Let  each  observer  take  the  distance  of 
the  Moon's  centre  from  his  zenith,  by  means  of  n 
exceeding  good  instrument,  at  the  moment  oi  ;>er 
passing  the  meridian:  add  these  two  zenith-distan- 
ces of  the  Moon  together,  and  iheir  excess  above  the 


468  The  Method  of  finding  the  Distances 

distance  between  the  two  zeniths  will  be  the  distance 
between  the  two  apparent  places  of  the  Moon. 
Then,  as  the  sum  of  the  natural  sines  ot  the  two  ze- 
nith-distances of  the  Moon  is  to  radius,  so  is  the 
distance  between  her  two  apparent  places  to  her  hori- 
zontal parallax  :'  which  being  found,  her  distance 
from  the  Earth's  centre  may  be  found  by  the  anal- 
ogy mentioned  in  $  4. 

Thus,  in  Fig.  2.  let  FECQ.  be  the  Earth,  Jl/the 
Moon,  and  Zbaz  an  arc  of  the  celestial  meridian. 
Let  ^be  Vienna,  whose  latitude  EVi*  48°  20'  north ; 
and  C  the  Cape  of  Good  Hope,  whose  latitude  EC 
is  34°  30'  south  :  both  which  latitudes  we  suppose 
to  be  accurately  determined  before-hand  by  the  ob- 
servers. As  these  two  places  are  on  the  same  me- 
ridian nVECs,  and  in  different  hemispheres,  the 
sum  of  their  latitudes  82°  50'  is  their  distance  from 
each  other.  Z  is  the  zenith  of  Vienna,  and  z  the  ze- 
nithof  the  Cape  of  Good  Hope  ;  which  two  zeniths 
are  also  82°  50'  distant  from  each  other,  in  the 
common  celestial  meridian  Zz.  To  the  observer 
at  Vienna,  the  Moon's  centre  will  appear  at  a  in  the 
celestial  meridian ;  and  at  the  same  instant,  to  the  ob- 
server at  the  Cape  it  will  appear  at  b.  Now-  sup- 
pose the  Moon's  distance  Za  from  the  zenith  of  Vi- 
enna to  be  38°  1'  53" ;  and  her  distance  zb  from  the 
zenith  of  the  Cape  of  Good  Hope  to  be  46°  4'  41"  : 
the  sum  of  these  two  zenith-distances  (Z  a+zb) 
is  84°  6'  34",  from  which  subtract  82°  50',  the 
distance  Zz  between  the  zeniths  of  these  two 
places,  and  there  will  remain  1°  16'  34"  for 
the  arc  ba,  or  distance  between  the  two  apparent 
places  of  the  Moon's  centre  as  seen  from  ^andfrom  C. 
Then,  supposing  the  tabular  radius  to  be  10000000, 
the  natural  sine  of  38°  1'  53"  (the  arc  ZaJ  is 
6160816,  and  the  natural  sine  of  46°  4'  41"  (the 
arc  Zb)  is  7202821  ;  the  sum  of  both  these 
sines  is  13363637.  Say,  therefore,  As  13363637 


cf  the  Planets  from  the  Sun.  '469 

is  to  10000000,  so  is  1°  16'  34"  to  47'  18",  which 
is  the  Moon's  horizontal  parallax. 

If  the  two  places  of  observation  be  not  exactly 
under  the  same  meridian,  their  difference  of  longi- 
tude must  be  accurately  taken,  that  proper  al- 
lowance may  be  made  for  the  Moon's  change  of 
declination  while  she  is  passing  from  the  meridian  of 
the  one  to  the  meridian  of  the  other. 

6.  The  Earth's  diameter,    as  seen  from  the 
Moon,  subtends  an  angle  of  double  the   Moon's 
horizontal   parallax ;     which   being   supposed  (as    . 
above)  to  be  51'  18",  or  3438",  the  Earth's  diam- 
eter must  be   1°  54''  36",  or  6876".      When  the 
Moon's  horizontsl  parallax  (which  is  variable  on 
account  of  the  eccentricity  of  her  orbit)  is  57'  18", 
her  diameter  subtends  an  angle  of  31'  2",  or  1862"  : 
therefore  the  Earth's  diameter  is  to  the  Moon's  di- 
ameter, as  6876  is  to  1862 ;  that  is,  as  3.69  is  to  1. 

And  since  the  relative  bulks  of  spherical  bodies 
are  as  the  cubes  of  their  diameters,  the  Earth's 
bulk  is  to  the  Moon's  bulk,  as  49.4  is  to  1. 

7.  The  parallax,  and  consequently  the  distance 
and  bulk  of  any  primary  planet,  might  be  found 
in  the  above  manner,  if  the  planet  were  near  enough 
to  the  Earth,  to  make  the  difference  of  its  two  ap- 
parent places  sufficiently  sensible :  but  the  nearest 
planet  is  too  remote  for  the  accuracy  required.     In 
order  therefore  to  determine  the  distances  and  rela- 
tive bulks  of  the  planets  with  any  tolerable  degree 
of  precision,  we  must  have  recourse  to  a  method 
less  liable  to  error :  and  this  the  approaching  tran- 
sit of  Venus  over  the  Sun's  disc  will  afford  us. 

8.  From  the  time  of  any  inferior  conjunction  of 
the  Sun  and  Venus  to  the  next,  is  583  days  22 
hours  7  minutes.  And  if  the  plane  of  Venus's  or- 
bit were  coincident  with  the  plane  of  the  ecliptic, 
she  would  pass  directly  between  the  Earth  and  the 
Sun  at  each  inferior  conjunction,  and  would  then 
appear  like  a  d*«*k  round  spot  on  the  Sun  for  ah 


470  The  Method  of  finding  the  Distances 

7  hours  and  3  quarters.  But  Venus's  orbit  (like 
the  Moon's)  only  intersects  the  ecliptic  in  two  op- 
posite points  called  its  nodes.  And  therefore  one 
half  of  it  is  on  the  north  side  of  the  ecliptic,  and 
the  other  on  the  south  :  on  which  account  Venus 
can  never  be  seen  on  the  Sun,  but  at  those  inferior 
conjunctions  which  happen  in  or  near  the  nodes  of 
her  orbit.  At  all  the  other  conjunctions,  she  either 
passes  above  or  below  the  Sun ;  and  her  dark  side 
being  then  toward  the  Earth,  she  is  invisible. — 
The  last  time  when  this  planet  was  seen  like  a  spot 
on  the  Sun,  was  on  the  24th  of  November,  old 
style,  in  the  year  1639. 

ARTICLE  IT. 

Shewing  hoiv  to  find  the  horizontal  parallax  of  Fc- 
nus  by  observation,  and  from  thence,  by  analogy , 
the  parallax  and  distance  of  the  Sun,  and  of  all 
the  planets  from  him. 

9.  In  Fig.  4.  of  Plate  XIV.  let  DBA  be  the 
Earth,  V  Venus,  and  TSR  the  eastern  limb  of  the 
Sun.  To  an  observer  at  B  the  point  /  of  that  limb 
will  be  on  the  meridian,  its  place  referred  to  the 
heaven  will  be  at  E,  and  Venus  will  appear  just 
within  it  at  S.  Bui,  at  the  same  instant,  to  an  ob- 
server at  A,  Venus  is  east  of  the  Sun,  in  the  right 
line  AVF ;  the  point  t  of  the  Sun's  limb  appears 
at  e  in  the  heavens,  and  if  Venus  were  then  visible, 
she  would  appear  at  F.  The  angle  CVA  is  the  hori- 
zontal parallax  of  Venus,  which  we  seek  ;  and  is 
equal  to  the  opposite  angle  FVE^  whose  measure  is 
the  arc  FE.  ASC  is  the  Sun's  horizontal  paral- 
lax, equal  to  the  opposite  angle  eSE,  whose  mea- 
sure is  the  arc  eE:  and  FAc  (the  same  as  VAvJ  is 
Venus's  horizontal  parallax  from  the  Sun,  which 
may  be  found  by  ob:ening  how  much  later  in  ab- 
solute time  her  total  ingress  on  the  Sun  is,  as  seen 
from  A,  than  as  seen  from  B,  which  is  the 


of  the  Planets  from  the  Sun.  471 

time  she  takes  to  move  from  V  to  v  in  her  orbit 
OVv. 

10.  It  appears  by  the  tables  of  Venus's  motion 
and  the  Sun's,  that  at  the  time  of  her  ensuing  tran- 
sit, she  will  move  4'  of  a  degree  on  the  Sun's  disc  in 
60  minutes  of  time  ;  and  therefore  she  will  move  4" 
of  a  degree  in  one  minute  of  time. 

Now  let  us  suppose,  that  A  is  90°  west  of  B,  so 
that  when  it  is  noon  at  B,  it  will  be  VI  in  the  morn- 
ing at  A;  that  the  total  ingress  as  seen  from  B  is  at 
1  minute  past  XII,  but  that  as  seen  from  A  it  is  at  7 
minutes  30  seconds  past  VI :  deduct  6  hours  for  the 
difference  of  meridians  of  A  and  J9,  and  the  remain- 
der will  be  6  minutes  30  seconds  for  the  time  by 
which  the  total  ingress  of  Venus  on  the  Sun  at  S  is 
later  as  seen  from  A  than  as  seen  from  B :  which 
time  being  converted  into  parts  of  a  degree  is  26", 
or  the  arc  Fe  of  Venus's  horizontal  parallax  from  the 
Sun :  for,  as  1  minute  of  time  is  to  4  seconds  of  a 
degree,  so  is  6i  minutes  of  time  to  26  seconds  of  a 
degree. 

11.  The  times  in  which  the  planets  perform  their 
annual  revolutions  about  the  Sun,  are  already  known 
by  observation. — From  these  times,  and  the  univer- 
sal power  of  gravity  by  which  the  planets  are  retained 
in  their  orbits,  it  is  demonstrable,  that  if  the  Earth's 
mean  distance  from  the  Sun  be  divided  into  100000 
equal  parts,  Mercury's  mean  distance  from  the  Sun 
must  be  equal  to  38710  of  these  parts — •  Venus's 
mean  distance  from  the   Sun,   to   72333 — Mars's 
mean  distance,  152369 — Jupiter's  520096 — and  Sa- 
turn's, 954006.     Therefore,  when  the  number  of 
miles  contained  in  the  mean  distance  of  any  planet 
from  the  Sun  is  known,  we  can,  by  these  propor- 
tions, find  the  mean  distance  in  miles  of  all  the  rest. 

12.  At  the  time  of  the  ensuing  transit,  the  Earth's 
distance  from  the  Sun  will  be  1015  (the  mean  dis- 
tance being  here  considered  as  1000),  and  Venus's 
distance  from  the  Sun  will  be  720  (the  mean  distance 

3O 


472  The  Method  of  finding  the  Distance* 

_  being  considered  as  723),  which  differences  from  the 

"  mean  distances  arise  from  the  elliptical  figure  of  the 

planets'  orbits — Subtract  726  parts  from  1015,  and 

there  will  remain  289  parts  for  Venus's  distance  from 

the  earth  at  that  time. 

13.  Now,  since  the  horizontal  parallaxes  of  the 
planets  are*  inversely  as  their  distances  from  the 
Earth's  centre,  it  is  plain,  that  as  Venus  will  be  be- 
tween the  Earth  and  the  Sun  on  the  day  of  her  tran- 
sit, and  consequently  her  parallax  will  be  then  great- 
er than  the  Sun's,  if  her  horizontal  parallax  can  be  on 
that  day  ascertained  by  observation,  the  Sun's  hori- 
zontal parallax  may  be  found,  and  consequently  his 
distance  from  the  Earth.- — Thus,  suppose  Venus's 
horizontal  parallax  should  be  found  to  be  36".S480; 
then,  As  the  Sun's  distance  1015  is  to  Venus's  dis- 
tance 289,  so  is  Venus's  horizontal  parallax  36". 
3480  to  the  Sun's  horizontal  parallax  10". 3493,  on  the 
day  of  her  transit.  And  the  difference  of  these  two 
parallaxes,  viz.  25".9987  (which  may  be  esteemed 
26")  will  be  the  quantity  of  Venus's  horizontal  paral- 
lax from  the  Sun ;  which  is  one  of  the  elements  for 
prejecting  or  delineating  her  transit  over  the  Sun's 
disc,  as  will  appear  further  on. 

To  find  the  Sun's  horizontal  parallax  at  the  time 
of  his  mean  distance  from  the  Earth,  say,  As  1000 
parts,  the  Sun's  mean  distance  from  the  Earth's 
centre,  is  to  1015,  his  distance  from  it  on  the 


*  To  prove  this,  let  S  be  the  Sun  (Fig-.  3.)  V  Venus,  AB  the  Earth, 
Cits  centre,  and  AC  its  semidiameter.  The  angle  AVC  is  the  hori- 
zontal parallax  of  Venus,  and  ASCthe  horizontal  parallax  of  the  Sun. 
But  by  the  property  of  plane  triangles,  as  the  sine  of  AVC  (or  of  SVA 
its  supplement  to  180)  is  to  the  .sine  of  AVC,  so  is  AS  to  AV,  and  so  is 
CS  to  CV. — N.  B.  In  all  angles  less  than  a  minute  of  a  degree,  the 
sines,  tangents,  and  arcs,  are  so  nearly  equal,  that  they  may,  without 
error  be  used  for  one  another.  And  here  we  make  use  of  Gardiner's 
logarithmic  tables,  because  they  have  the  sines  to  everyfcsecond  of  a 
degree. 


of  the  Planets  from  the  Sun. 

day  of  the  transit,  so  is  10",3493,  his  horizontal 
parallax  on  that  day,  to  10". 5045,  his  horizontal 
parallax  at  the  time  of  his  mean  distance  from  the 
Earth's  centre. 

14.  The  Sun's  parallax  being  thus  (or  any  other 
way  supposed  to  be)  found,  at  the  time  of  his  mean 
distance  from  the  Earth,  we  may  find  his  true  dis- 
tance from  it  in  semicliameters  of  the  Earth,  by  the 
following  analogy.  As  the  sine  (or  tangent  of  so 
small  an  arc  as  that)  of  the  Sun's  parallax  10".  5045 
is  to  radius,  so  is  unity,  or  the  Earth's  semidiameter, 
to  the  number  of  semidiameters  of  the  Earth  that  the 
Sun  is  distant  from  its  centre,  which  number,  being 
multiplied  by  3985,  the  number  of  miles  contained 
in  the  Earth's  semidiameter,  will  give  the  number  of 
miles  which  the  Sun  is  distant  from  the  Earth's 
centre. 

Then,  by  §  11,  As  100000,  the  Earth's  mean  dis- 
tance from  the  Sun  in  parts,  is  to  38710,  Mercury's 
mean  distance  from  the  Sun  in  parts,  so  is  the  Earth's 
mean  distance  from  the  Sun  in  miles  to  Mercury's 
mean  distance  from  the  Sun  in  miles. — And, 

As  100000  is  to  72333,  so  is  the  Earth's  mean 
distance  from  the  Sun  in  miles  to  Venus's  mean  dis- 
tance from  the  Sun  in  miles. — Likewise, 

As  100000  is  to  152369,  so  is  the  Earth's  mean 
distance  from  the  Sun  in  miles  to  Mars's  mean  dis- 
tance from  the  Sun  in  miles. — Again, 

As  100000  is  to  520096,  so  is  the  Earth's  mean 
distance  from  the  Sun  in  miles  to  Jupiter's  mean  dis- 
tance from  the  Sun  in  miles. — Lastly, 

As  100000  is  to  954006,  so  is  the  Earth's  mean 
distance  from  the  Sun  in  miles  to  Saturn's  mean  dis- 
tance from  the  Sun  in  miles. 

And  thus,  by  having  found  the  distance  of  any 
one  of  the  planets  from  the  Sun,  we  have  sufficient 
data  for  finding  the  distances  of  all  the  rest. — And 
then  from  their  apparent  diameters  at  these  known 


474  The  Method  of  finding  the  Distances 

distances,  their  real  diameters  and  bulks  may  be 
found. 

15.  The  Earth's  diameter,  as  seen  from  the  Sun, 
subtends  an  angle  of  double  the  Sun's  horizontal 
parallax,  at  the  time  of  the  Earth's  mean  distance 
from  the  Sun  :  and  the  Sun's  diameter,  as  seen  from 
the  Earth  at  that  time,  subtends  an  angle  of  32'  2", 
or  1922".     Therefore  the  Sun's  diameter  is  to  the 
Earth's  diameter,  as  1922  is  to  21. — And  since  the 
relative  bulks  of  spherical  bodies  are  as  the  cubes  of 
their  diameters,  the  Sun's  bulk  is  to  the  Earth's  bulk, 
as  756058  is  to  1 ;  supposing  the  Sun's  mean  hori- 
zontal parallax  to  be  10". 5,  as  above. 

16.  It  is  plain  by  Fig.  4.  that  whether  Venus  be 
at  If  or  V,  or  in  any  other  part  of  the  right  line  BVS> 
it  will  make  no  difference  in  the  time  of  her  total  in- 
gress on  the  Sun  at  £,  as  seen  from  2?;  but  as  seen 
from  A  it  will.    For,  if  Venus  be  at  V,  her  horizon- 
tal parallax  from  the  Sun  is  the  arc  Fey  which  mea- 
sures the  angle  FAe :  but  if  she  be  nearer  the  Earth, 
as  at  U)  her  horizontal  parallax  from  the  Sun  is  the 
arc/£,  which  measures  the  angle  fAe;  and  this  angle 
is  greater  than  the  angle  FAey  by  the  difference  of 
their  measures  fF.     So  that,  as  the  distance  of  the 
celestial  object  from  the  Earth  is  less,  its  parallax  is 
the  greater. 

17.  To  find  the  parallax  of  Venus  by  the  above 
method,  it  is  necessary,  1.  That  the  difference  of 
meridians  of  the  two  places  of  observation  be  90°. 
— 2.  That  the  time  of  Venus's  total  ingress  on  the 
Sun  be  when  his  eastern  limb  is  either  on  the  me- 
ridian of  one  of  the  places,  or  very  near  it. — And, 
3.  That  each  observer  have  his  clock  exactly  regu- 
lated to  the  equal  time  at  his  place.     But  as  it 
might,  perhaps,  be  difficult  to  find  two  places  on 
the  Earth  suited  to  the  first  and  second  of  these  re- 
quisites, we  shall  shew  how  this  important  problem 
may  be  solved  by  a  single  observer,  if  he  be  exact 


of  the  Planets  from  the  Sun.  475 

as  to  his  longitude,  and  have  his  clock  truly  adjusted 
to  the  equal  time  at  his  place. 

18.  That  part  of  Venus's  orbit  in  which  she  will 
move  during  her  transit  on  the  Sun,  may  be  consi- 
dered as  a  straight  line ,  and  therefore,  a  plane  may  be 
conceived  to  pass  both  through  it  and  the  Earth's 
centre.  To  every  place  on  the  Earth's  surface  cut 
by  this  plane,  Venus  will  be  seen  on  the  Sun  in  the 
same  path  that  she  would  describe  as  seen  from  the 
Earth's  centre ;  and  therefore  she  will  have  no  pa- 
rallax of  latitude,  either  north  or  south  ;  but  will  have 
a  greater  or  less  parallax  of  longitude,  as  she  is  more 
or  less  distant  from  the  meridian,  at  any  time  during  - 
her  transit. 

Matura,  a  town  and  fort  on  the  south  coast  of  the 
island  of  Ceylon,  will  be  in  this  plane  at  the  time  of 
Venus's  total  ingress  on  the  Sun ;  and  the  Sun  will 
then  be  621°  east  of  the  meridian  of  that  place.  Con- 
sequently to  an  observer  at  Matura,  Venus  will  have 
a  considerable  parallax  of  longitude  eastward  from 
the  Sun,  when  she  would  appear  to  touch  the  Sun's 
eastern  limb  as  seen  from  the  Earth's  centre,  at 
which  the  astronomical  tables  suppose  the  observer 
to  be  placed,  and  give  the  times  as  seen  from  thence. 

19.  According  to  these  tables,  Venus's  total  in- 
gress on  the  Sun  will  be  50  minutes  after  VII  in  the 
morning,  at  Matura*,  supposing  that  place  to  be  80° 
east  longitude  from  the  meridian  of  London,  which  is 
the  observer's  business  to  determine.  Let  us  ima- 
gine that  he  finds  it  to  be  exactly  so,  but  that  to  him 
the  total  ingress  is  at  VII  hours  55  minutes  46  se- 
conds, which  is  5  minutes  46  seconds  later  than  the 
true  calculated  time  of  total  ingress,  as  seen  from  the 
Earth's  centre.  Then,  as  Venus's  motion  on  (or 


*  The  time  of  total  ingress  at  London,  as  seen  from  the  Earth's  cen- 
tre, is  at  30  minutes  after  II  in  the  morning ;  and  if  Matura  be  just 
80°  (or  5  hours  20  minutes)  east  of  London,  when  it  is  30  minutes  past 
II  in  thft  morning1  at  Lendm,  it  is  5U  minutes  past  VII  at  Matxra* 


476  The  Method  of  finding  the  Distances 

toward,  or  from)  the  Sun  is  at  the  rate  of  4  minutes 
of  a  degree  in  an  hour  (by  $  10.)  her  motion  must  be 
23".  1  of  a  degree  in  5  minutes  46  seconds  of  time: 
and  this  23".  1  is  her  parallax  eastward,  from  her  to- 
tal ingress  as  seen  from  Matura,  when  her  ingress 
would  be  total  if  seen  from  the  Earth's  centre. 

20.  At  VII  hours  50  minutes  in  the  morning,  the 
Sun  is  62^°  from  the  meridian ;  at  VI  in  the  morn- 
ing he  is  90°  from  it :  therefore,  as  the  sine  of  62|° 
is  to  the  sine  of  23".  1  (which  is  Venus's  parallax 
from  her  .true  place  on  the  Sun  at  VII  hours  50  mi- 
nutes),  so  is  radius  or  the  sine  of  90°,  to  the  sine  of 
26",  which  is  Venus's  horizontal  parallax  from  the 
Sun  at  VI.  In  logarithms  thus  : 

As  the  logarithmic  sine  of  62<>  30'  -  -  -  9.9479289 
Is  to  the  logarithmic  sine  of  23".l  -  -  -  6.0481510 
So  is  the  logarithmic  radius  -  -  -  10.0000000 


To  the  logarithmic  sine  of  26"  very  nearly  -        6.1002221 

Divide  the  Sun's  distance  from  the  Earth,  1015, 
by  his  distance  from  Venus  726  (5  12.)  and  the  quo- 
tient  will  be  1.3980;  which  being  multiplied  by 
Venus's  horizontal  parallax  from  the  Sun  26",  will 
give  36". 3480,  for  her  horizontal  parallax  as  seen 
from  the  Earth  at  that  time. — Then  (by  §  13.)  as  the 
Sun's  distance,  1015,  is  to  Venus's  distance  289,  so 
is  Venus's  horizontal  parallax  36". 3480  to  the  Sun's 
horizontal  parallax  10".  3493. — If  Venus's  horizontal 
parallax  from  the  Sun  be  found  by  observation  to  ba 
greater  or  less  than  26",  the  Sun's  horizontal  parallax 
must  be  greater  or  less  than  10".3493  accordingly. 

21.  And  thus,  by  a  single  observation,  the  parallax 
of  Venus,  and  consequently  the  parallax  of  the  Sun, 
might  be  found,  if  we  were  sure  that  the  astronomi- 
cal tables  were  quite  correct  as  to  the  time  of  Venus's 
total  ingress  on  the  Sun. — But  although  the  tables 
may  be  safely  depended  upon  for  shewing  the  true 


of  the  Planets  from  the  Sun. 

duration  of  the  transit,  which  will  not  be  quite  6  hours 
from  the  time  of  Venus's  total  ingress  on  the  Sun's 
eastern  limb,  to  the  beginning  of  her  egress  from  his 
western ;  yet  they  may  perhaps  not  give  the  true 
times  of  these  two  internal  contacts :  like  a  good 
common  clock,  which,  though  it  may  be  trusted  to 
for  measuring  a  few  hours  of  time,  yet  perhaps  it  may 
not  be  quite  adjusted  to  the  meridian  of  the  place, 
and  consequently  not  true  as  to  any  one  hour  ;  which 
every  one  knows  is  generally  the  case. — Therefore,  to 
make  sure  work,  the  observer  ought  to  watch  both 
the  moment  of  Venus's  total  ingress  on  the  Sun, 
and  her  beginning  of  egress  from  him,  so  as  to  note 
precisely  the  times  between  these  two  instants,  by 
means  of  a  good  clock :  and  by  comparing  the  inter- 
val at  his  place  with  the  true  calculated  interval  as 
seen  from  the  Earth's  centre,  which  will  be  5  hours 
58  minutes,  he  may  find  the  parallax  of  Venus  from 
the  Sun  both  at  her  total  ingress  and  beginning  of 
egress. 

22.  The  manner  of  observing  the  transit  should  be 
as  follows : — The  observer  being  provided  with  a 
good  telescope,  and  a  pendulum-clock  well  adjusted 
to  the  mean  diurnal  revolution  of  the  Sun,  and  as 
near  to  the  time  at  his  place  as  conveniently  may  be; 
and  having  an  assistant  to  watch  the  clock  at  the 
proper  times,  he  must  begin  to  observe  the  Sun's 
eastern  limb  through  his  telescope,  twenty  minutes 
at  least  before  the  computed  time  of  Venus's  total  in- 
gress upon  it,  lest  there  should  be  an  error  in  the 
time  of  the  beginning  as  given  by  the  tables. 

When  he  perceives  a  dent  (as  it  were)  to  be  made 
in  the  Sun's  limb,  by  the  interposition  of  the  dark 
body  of  Venus,  he  must  then  continue  to  watch  her 
through  the  telescope  as  the  dent  increases ;  and  his 
assistant  must  watch  the  time  shewn  by  the  clock, 
till  the  whole  body  of  the  planet  appears  just  within 
the  Sun's  limb :  and  the  moment  when  the  bright 
limb  of  the  Sun  appears  close  by  the  east  side  of  the 


The  Method  of  finding  the  Distances 

dark  limb  of  the  planet,  the  observer,  having  a  little 
hammer  in  his  hand,  is  to  strike  a  blow  therewith  on 
the  table  or  wall ;  the  moment  of  which,  the  assist- 
ant notes  by  the  clock,  and  writes  it  down. 

Then,  let  the  planet  pass  on  for  about  2  hours  59 
minutes,  in  which  time  it  will  be  got  to  the  middle  of 
its  apparent  path  on  tire  Sun,  and  consequently  will 
then  be  at  its  least  apparent  distance  from  the  Sun's 
centre  ;  at  which  time,  the  observer  must  take  its  dis- 
tance from  the  Sun's  centre  by  means  of  a  good  mi- 
crometer, in  order  to  ascertain  its  true  latitude  or  de- 
clination from  the  ecliptic,  and  thereby  find  the  places 
of  its  nodes. 

This  done,  there  is  but  little  occasion  to  observe 
it  any  longer,  until  it  comes  so  near  the  Sun's  western 
limb,  as  almost  to  touch  it.  Then  the  observer  must 
watch  the  planet  carefully  with  his  telescope. :  and  his 
assistant  must  watch  the  clock,  so  as  to  note  the 
precise  moment  of  the  planet's  touching  the  Sun's 
limb,  which  the  assistant  knows  by  the  observer  strik- 
ing a  blow  with  his  hammer. 

23.  The  assistant  must  be  very  careful  in  observing 
what  minute  on  the  dial-plate  the  minute-hand  has  past, 
when  he  has  observed  the  second-hand  at  the  instant 
the  blow  was  struck  by  the  hammer;  otherwise,  though 
he  be  tight  as  to  the  number  of  seconds  of  the  current 
minute,  he  may  be  liable  to  make  a  mistake  in  the  num- 
ber of  minutes. 

24.  To  those  places  where  the  transit  begins  before 
XII  at  noon,  and  ends  after  it,  Venus  will  have  an 
eastern  parallax  from  the  Sun  at  the  beginning,  and 
a  western  parallax  from  the  Sun  at  the  end ;  which 
will  contract  the  duration  of  the  transit,    by    caus- 
ing it  to  begin  later  and  end  sooner,  at  these  places, 
than  it  does  as  seen  from  the  Earth's  centre ;  which  may- 
be explained  in  the  following  manner. 


of  the  Planets  from  the  Sun.  479 

In  Fig.  5.  of  Plate  XIV  let  BMA  be  the  Earth, 
V  Venus,  and  S  the  Sun.  The  Earth's  motion  on 
its  axis  from  west  to  east,  or  in  the  direction 
A  MB,  carries  an  observer  on  that  side  contrary 
to  the  motion  of  Venus  in  her  orbit,  which  is  in 
the  direction  UVW;  and  will  therefore  cause  her 
motion  to  appear  quicker  on  the  Sun's  disc,  than 
it  would  appear  to  an  observer  placed  at  the  Earth's 
centre  C,  or  at  either  of  its  poles.  For,  if  Venus 
were  to  stand  still  in  her  orbit  at  V  for  twelve  hours, 
the  observer  on  the  Earth's  surface  would  in  that 
time  be  carried  from  A  to  B,  through  the  arc  AMB* 
When  he  was  at  A,  he  would  see  Venus  on  the  Sun 
at  R;  when  at  M,  he  would  see  her  at  S;  and  when 
he  was  at  B,  he  would  see  her  at  T:  so  that  his  own 
motion  would  cause  the  planet  to  appear  in  motion  on 
the  Sun  through  the  line  RST;  which  being  in  the 
direction  of  her  apparent  motion  on  the  Sun  as  she 
moves  in  her  orbit  UJV,  her  motion  will  be  accele* 
rated  on  the  Sun  to  this  observer,  just  as  much  as  his 
own  motion  would  shift  her  apparent  place  on  the 
Sun,  if  she  were  at  rest  in  her  orbit  at  V. 

But  as  the  whole  duration  of  the  transit,  from  first 
to  last  internal  contact,  will  not  be  quite  six  hours; 
an  observer,  who  has  the  Sun  on  his  meridian  at  the 
middle  of  the  transit,  will  be  carried  only  from  a  to  b 
during  the  whole  time  thereof.  And  therefore,  the 
duration  will  be  much  less  contracted  by  his  own 
motion,  than  if  the  planet  were  to  be  twelve  hours  in 
passing  over  the  Sun,  as  seen  from  the  Earth's 
centre. 

25.  The  nearer  Venus  is  to  the  Earth,  the  greater 
is  her  parallax,  and  the  more  will  the  true  duration  of 
her  transit  be  contracted  thereby ;  the  farther  she  is 
from  the  Earth,  the  contrary :  so  that  the  contraction 
will  be  in  direct  proportion  to  the  parallax.  There- 
fore, by  observing,  at  proper  places,  how  much  the 
duration  of  the  transit  is  less  than  its  true  duration  at 
the  Earth's  centre,  where  it  is  5  hours  58  minutes, 

3P 


180  The  Method  of  finding  the  Distances 

as  given  by  the  astronomical  tables,  the  parallax  of 
Venus  will  be  ascertained. 

26.  The  above  method  (§  17,  Of  seq.}  is  much 
the  same  as  was  prescribed  long  ago  by  Doctor  Hal- 
ley  ;  but  the  calculations  differ  considerably  from  his ; 
as  will  appear  in  the  next  article,  which  contains  a 
translation  of  the  Doctor's  whole  dissertation  on  that 
subject.— He  had  not  computed  his  own  tables  when  he 
wrote  it,  nor  had  he  time  before -hand  to  make  a  suffi- 
cient number  of  observations  on  the  motion  of  Venus, 
so  as  to  determine  whether  the  nodes  of  her  orbit  are 
at  rest  or  not ;  and  wras  therefore  obliged  to  trust  to 
other  tables,  which  are  now  found  to  be  erroneous. 

ARTICLE  III. 

Containing  Doctor  HAL  LEY'S  Dissertation  on  the 
method  of  finding  the  Sun^s  parallax  and  distance 
from  the  Earth,  .by  the  transit  of  Venus  over  the 
Sun's  disc,  June  the  6th,  1761.  Translated  from 
the  Latin  in  Mottee's  Abridgment  of  the  Philoso- 
phical Transactions,  Vol.  I.  page  243  ;  with  addi- 
tional notes. 

There  are  many  things  exceedingly  paradoxical, 
and  that  seem  quite  incredible  to  the  illiterate,  which 
yet  by  means  or  mathematical  principles  may  be  easily 
solved.  Scarce  any  problem  will  appear  more  hard 
and  difficult,  than  that  of  determining  the  distance  of 
the  Sun  from  the  Earth  very  near  the  truth  :  but  even 
this,  when  we  are  made  acquainted  with  some  exact 
observations,  taken  at  places  iixed  upon,  and  chosen 
before-hand,  will  without  much  labour  be  effected. 
And  this  is  what  I  am  now  desirous  to  lay  before  this 
illustrious  Society*  (which  I  foretel  will  continue  for 
ages),  that  I  may  explain  before-hand  to  young  astro- 
nomers, who  may  perhaps  live  to  observe  these  things, 

*  The  Royal  Society. 


of  the  Planets  from  the  Sun.  481 

a  method  by  which  the  immense  distance  of  the  Sun 
may  be  truly  obtained,  to  within  a  five-hundredth  part 
of  what  it  really  is. 

It  is  well  known  that  the  distance  of  the  Sun  from 
the  Earth  is  by  different  astronomers  supposed  diffe- 
rent, according  to  what  was  judged  most  probable 
from  the  best  conjecture  that  each  could  form.  Pto- 
lemy and  his  followers,  as  also  Copernicus  and  Tycho 
.Brake,  thought  it  to  be  1200  semidiameters  of  the 
Eanh;  Kepler,  3500  nearly:  Ricciolus  doubles  the 
distance  mentioned  by  Kepler  ;  and  Hevelius  only  in- 
creases it  by  one  half.  But  the  planets  Venus  and 
Mercury  having,  by  the  assistance  of  the  telescope, 
been  seen  on  the  disc  of  the  Sun,  deprived  of  their 
borrowed  brightness,  it  is  at  length  found  that  the  ap-  . 
parent  diameters  of  the  planets  are  much  less  than  they 
were  formerly  supposed ;  and  that  the  semidiameter  of 
Venus  seen  from  the  Sun  subtends  an  angle  of  no  more 
than  a  fourth  part  of  a  minute,  or  15  seconds,  while  the 
semidiameter  of  Mercury,  at  its  mean  distance  from 
the  Sun,  is  seen  under  an  angle  only  of  ten  seconds ; 
that  the  semidiameter  of  Saturn  seen  from  the  Sun 
appears  under  the  same  angle ;  and  that  the  semidia- 
meter of  Jupiter,  the  largest  of  all  the  planets,  sub- 
tends an  angle  of  no  more  than  a  third  part  of  a  minute 
at  the  Sun.  Whence,  keeping  the  proportion,  some 
modern  astronomers  have  thought,  that  the  semidia- 
meter of  the  Earth,  seen  from  the  Sun,  would  sub- 
tend a  mean  angle  between  that  larger  one  subtended 
by  Jupiter,  and  that  smaller  one  subtended  by  Saturn 
and  Mercury ;  and  equal  to  that  subtended  by  Venus 
(namely,  fifteen  seconds) :  and  have  thence  concluded, 
that  the  Sun  is  distant  from  the  Karth  almost  14000 
of  the  Earth's  semidiameters.  But  the  same  authors 
have  on  another  account  somewhat  increased  this 
distance:  for  inasmuch  as  the  Moon's  diameter  is 
a  little  more  than  a  fourth  part  of  the  diameter  of 
the  Earth,  if  the  Sun's  parallax  should  be  supposed 


The  Method  of  finding  the  Distances 

fifteen  seconds,  it  would  follow  that  the  body  of  the 
Moon  is  larger  than  that  of  Mercury ;  that  is,  that  a 
secondary  planet  would  be  greater  than  a  primary ; 
which  would  seem  inconsistent  with  the  uniformity  of 
the  mundane  system.  And  on  the  contrary,  the  same 
regularity  and  uniformity  seems  scarcely  to  admit  that 
Venus,  an  inferior  planet,  that  has  no  satellite,  should 
be  greater  than  our  Earth,  which  stands  higher  in  the 
system,  and  has  such  a  splendid  attendant.  There- 
fore, to  observe  a  mean,  let  us  suppose  the  semidia- 
meter  of  the  Earth  seen  from  the  Sun,  or,  which  is  the 
same  thing,  the  Sun's  horizontal  parallax,  to  be  twelve 
seconds  and  a  half;  according  to  which,  the  Moon 
\  will  be  less  than  Mercury,  and  the  Earth  larger  than 
Venus ;  and  the  Sun's  distance  from  the  Earth  will 
come  out  nearly  16, 500  of  the  Earth's  semidiameters. 
This  distance  I  assent  to  at  present,  as  the  true  one, 
till  it  shall  become  certain  what  it  is,  by  the  experi- 
ment which  I  propose.  Nor  am  I  induced  to  alter 
my  opinion  by  the  authority  of  those  (however  weighty 
it  may  be)  who  are  for  placing  the  Sun  at  an  immense 
distance  beyond  the  bounds  here  assigned,  relying  on 
observations  made  upon  the  vibrations  of  a  pendulum, 
in  order  to  determine  those  exceeding  small  angles ; 
but  which,  as  it  seems,  are  not  sufficient  to  be  depend- 
ed upon  ;  at  least,  by  this  method  of  investigating  the 
parallax,  it  will  sometimes  come  out  nothing,  or  even 
negative ;  that  is,  the  distance  would  either  become 
infinite,  or  greater  than  infinite  ;  which  is  absurd.  And 
indeed,  to  confess  the  truth,  it  is  hardly  possible  for  a 
man  to  distinguish,  with  any  degree  of  certainty,  se- 
conds, or  even  ten  seconds,  with  instruments,  let  them 
be  ever  so  skilfully  made :  therefore,  it  is  not  at  all  to 
be  wondered  at,  that  the  excessive  nicety  of  this  mat- 
ter has  eluded  the  many  and  ingenious  endeavours  of 
such  skilful  operators. 

About  forty  years  ago,  while  I  was  in  the  island 
of  St.  Helena^  observing  the  stars  about  the  south 


of  the  Planets  from  the  Sun. 

pole,  I  had  an  opportunity  of  observing,  with  the  great- 
est diligence,  Mercury  passing  over  the  disc  of  the 
Sun  ;  and  (which  succeeded  better  than  1  could  have 
hoped  for)  I  observed,  with  the  greatest  degree  of  ac- 
curacy, by  means  of  a  telescope  24  feet  long,  the  very 
moment  when  Mercury  entering  upon  the  Sun  seemed 
to  touch  its  limb  within,  and  also  the  moment  when 
going  off  it  struck  the  limb  of  the  Sun's  disc,  form- 
ing the  angle  of  interior  contact :  whence  I  found  the 
interval  of  time,  during  which  Mercury  then  appeared 
within  the  Sun's  disc,  even  without  an  error  of  one 
second  of  time.  For  the  lucid  line  intercepted  between 
the  dark  limb  of  the  planet  and  the  bright  limb  of  the 
Sun,  although  exceeding  fine,  is  seen 'by  the  eye ;  and 
the  little  dent  made  in  the  Sun's  limb,  by  Mercury's 
entering  the  disc,  appears  to  vanish  in  a  moment ;  and 
also  that  made  by  Mercury,  when  leaving  the  disc, 
seems  to  begin  in  an  instant. — When  I  perceived  this, 
it  immediately  came  into  my  mind,  that  the  Sun's 
parallax  might  be  accurately  determined  by  such  kind 
of  observations  as  these ;  provided  Mercury  were  but 
nearer  to  the  Earth,  and  had  a  greater  parallax  from 
the  Sun ;  but  the  difference  of  these  parallaxes  is  so 
little,  as  always  to  be  less  than  the  solar  parallax  which 
we  see ;  and  therefore  Mercury,  though  frequently  to 
be  seen  on  the  .Sun,  is  not  to  be  looked  upon  as  lit 
for  our  purpose. 

There  remains  then  the  transit  of  Venus  over  the 
Sun's  disc ;  whose  parallax,  being  almost  four  times  as 
great  as  the  solar  parallax,  will  cause  very  sensible  dif- 
ferences between  the  times  in  which  Venus  will  seem 
to  be  passing  over  the  Sun  at  different  parts  of  the 
Earth.  And  from  these  differences,  if  they  be  observ- 
ed as  they  ought,  the  Sun's  parallax  may  be  deter- 
mined even  to  a  small  part  of  a  second.  Nor  do  we 
require  any  other  instruments  for  this  purpose,  than 
common  telescopes  and  clocks,  only  good  of  their 
kind  :  and  in  the  observers,  nothing  more  is  needful 


434  The  Method  of  finding  the  Distances 

than  fidelity,  diligence,  and  a  moderate  skill  in  astrono- 
my. For  there  is  no  need  that  the  latitude  of  the  place 
should  be  scrupulously  observed,  nor  that  the  hours 
themselves  should  be  accurately  determined  with  re- 
spect to  the  meridian :  it  is  sufficient  that  the  clocks 
IDC  regulated  according  to  the  motion  of  the  heavens, 
if  the  times  be  well  reckoned  from  the  total  ingress  of 
Venus  into  the  Sun's  disc,  to  the  beginning  of  her 
egress  from  it ;  that  is,  when  the  dark  globe  of  Venus 
first  begins  to  touch  the  bright  limb  of  the  Sun  with- 
in ;  which  moments,  I  know,  by  my  own  experience, 
may  be  observed  within  a  second  of  time. 

But  on  account  of  the  very  strict  laws  by  which  the 
motions  of  the  planets  are  regulated,  Venus  is  seldom 
seen  within  the  Sun's  disc ;  and  during  the  course  of 
more  than  120  years,  it  could  not  be  seen  once ; 
namely,  from  the  year  1639  (when  this  most  pleasing 
sight  happened  to  that  excellent  youth,  fforrox,  our 
countryman,  and  to  him  only,  since  the  creation)  to 
the  year  1761 ;  in  which  year,  according  to  the  theo- 
ries which  we  have  hitherto  found  agreeable  to  the 
celestial  motions,  Venus  will  again  pass  over  the  Sun 
on  the*  26th  of  May,  in  the  morning;  so  that  at  Lon- 
don,  about  six  o'clock  in  the  morning,  we  may  expect 
to  see  it  near  the  middle  of  the  Sun's  disc,  and  not 
above  four  minutes  of  a  degree  south  of  the  Sun's 
centre.  But  the  duration  of  this  transit  will  be  almost 
eight  hours ;  namely,  fmrfi  two  o'clock  in  the  morn- 
ing till  almost  ten.  Hence  the  ingress  will  not  be 
visible  in  England;  but  as  the  Sun  will  at  that 
time  be  in  the  16th  degree  of  Gemini,  having  almost 
23  degrees  north  declination,  it  will  be  seen  without 
setting  at  all  in  almost  all  parts  of  the  north  frigid 
zone :  and  therefore  the  inhabitants  of  the  coast  of 
Norway,  beyond  the  city  of  Nidrosia,  which  is  called 
Dronthdm,  as  far  as  the  North  Cape,  will  be  able  to 
observe  Venus  entering  the  Sun's  disc ;  and  perhaps 

*  The  sixth  of  June,  according  to  the  new  style. 


of  the  Planets  from  the  Sun.  485 

the  ingress  of  Venus  upon  the  Sun,  when  rising,  will 
be  seen  by  the  Scotch,  in  the  northern  parts  of  the 
kingdom,  and  by  the  inhabitants  of  the  Shetland hies -, 
formerly  called  Thule.  But  at  the  time  when  Venus 
will  be  nearest  the  Sun's  centre,  the  Sun  will  be  ver- 
tical to  the  northern  shores  of  the  bay  of  Bengal*  or 
rather  over  the  kingdom  tfPcgu;  and  therefore  in  the 
adjacent  regions,  as  the  Sun,  when  Venus  enters  his 
disc,  will  be  almost  four  hours  towards  the  east,  and 
as  many  toward  the  west  when  she  leaves  him,  the 
apparent  motion  of  Venus  on  the  Sun  will  be  accele- 
rated by  almost  double  the  horizontal  parallax  of 
Venus  from  the  Sun  ;  because  Venus  at  that  time  is 
carried  with  a  retrograde  motion  from  east  to  west, 
while  an  eye  placed  upon  the  Earth's  surface  is  whirl- 
ed the  contrary  way,  from  west  to  east*. 


*  This  has  been  already  taken  notice  of  in  §  24  ;  but  I  shall  here  en- 
deavour  to  explain  it  more  at  large,  together  with  some  of  the  follow- 
ing part  of  the  Doctor's  Essay,  by  a  figure. 

In  Fig.  1.  of  Plate  XV  let  Cbe  the  centre  of  the  Earth,  and  Z  the 
centre  of  the  Sun.  In  the  right  line  CvZ,  make  vZ  to  CZ  as  726  is  to 
1015  (§  12).  Let  acbdbe  the  Earth,  v  Venus's  place  in  her  orbit  at  the 
time  of  her  conjunction  with  the  Sun  ;  and  let  TSUbz  the  Sun,  whose 
diameter  is  31'  42". 

The  motion  of  Venus  in  her  orbit  is  in  the  direction  Nvn,  and  the 
Earth's  motion  on  its  axis  is  according  to  the  order  of  the  24  hours 
placed  around  it  in  the  figure.  Therefore,  supposing  the  mouth  of  the 
Ganges  to  be  at  G,  when  Venus  is  at  E  in  her  orbit,  and  to  be  carried 
from  G  to  £  by  the  Earth's  motion  on  its  axis,  while  Venus  moves  from 
JE  to  e  in  her  orbit ;  it  is  plain  that  the  motions  of  Venus  and  the  Ganges 
are  contrary  to  each  other. 

The  true  motion  of  Venus  in  her  orbit,  and  consequently  the  space 
she  seems  to  run  over  on  the  Sun's  disc  in  any  given  time,  could  be 
seen  only  from  the  Earth's  centre  C,  which  is  at  rest  with  respect  to 
its  surface.  And  as  seen  from  C,  her  path  on  the  Sun  would  be  in  the 
right  line  TtU ;  and  her  motion  therein  at  the  rate  of  four  minutes  of  a 
degree  in  an  hour.  T  is  the  point  of  the  Sun's  eastern  limb  which 
Venus  seems  to  touch  at  the  moment  of  her  total  ingress  on  the  Sun, 
as  seen  from  Cj  when  Venus  is  at  E  in  her  orbit;  and  U  is  the  point  of 
the  Sun's  western  limb  which  she  seems  to  touch  at  the  moment  of  her 
beginning  of  egress  from  the  Sun,  as  seen  from  C,  when  she  is  at  c  in 
ber  orbit. 


486  The  Method  of  finding  the  Distances 

Supposing  the  Sun's  parallax  (as  we  have  said) 
to  be  12-1",  the  parallax  of  Venus  will  be  43"; 
from  which  subtracting  the  parallax  of  the  Sun, 
there  will  remain  30"  at  least  for  the  horizontal 
parallax  of  Venus  from  the  Sun  ;  and  therefore  the 
motion  of  Venus  will  be  increased  45"  at  least  by 
that  parallax,  while  she  passes  over  the  Sun's  disc, 
in  those  elevations  of  the  pole  which  are  in  places 
near  the  tropic,  and  yet  more  in  the  neighbour- 
hood of  the  equator.  Now  Venus  at  that  time 
will  *move  on  the  sun's  disc,  very  nearly  at  the 
rate  of  four  minutes  of  a  degree  in  an  hour ;  and 
therefore  11  minutes  of  time  at  least  are  to  be 
allowed  for  45",  or  three  fourths  of  a  minute  of 


When  the  mouth  of  the  Ganges  is  at  m  (in  revolving  through  the 
arc  Gmg)  the  Sun  is  on  its  meridian.  Therefore,  since  G  and  g  are 
equally  distant  from  m  at  the  beginning  and  ending  of  the  transit,  it  is 
plain  that  the  Sun  will  be  as  far  east  of  the  meridian  of  the  Ganges 
(at  G)  when  the  transit  begins,  as  it  will  be  west  of  the  meridian  of 
the  same  place  (revolving  from  G  to  £•)  when  the  transit  ends. 

But  although  the  beginning  of  the  transit,  or  rather  the  moment  of 
Venus's  total  ingress  upon  the  Sun  at  T,  as  seen  from  the  Earth's 
centre,  must  be  when  Venus  is  at.E  in  her  orbit,  because  she  is  then 
seen  in  the  direction  of  the  right  line  GET,-  yet  at  the  same  instant  of 
time,  as  seen  from  the  Ganges  at  G,  she  will  be  short  of  her  ingress  on 
the  Sun,  being  then  seen  eastward  of  him,  in  the  right  line  GEKt 
which  makes  the  angle  KET  (equal  to  the  opposite  angle  GEC),  with 
the  right  line  GET.  This  angle  is  called  the  angle  of  Venus's  parallax 
from  the  Sun,  which  retards  the  beginning  of  the  transit  as  seen  from 
the  banks  of  the  Ganges  ;  so  that  the  Ganges  G,  must  advance  a  little 
farther  toward  m,  and  Venus  must  move  on  in  her  orbit  from  E  to  R, 
before  she  can  be  seen  from  G  (in  the  right  line  GRT)  wholly  within 
the  Sun's  disc  at  T. 

When  Venus  comes  to  e  in  her  orbit,  she  will  appear  at  U, 
as  seen  from  the  Earth's  centre  C,  just  beginning  to  leave  the 
Sun;  that  is,  at  the  beginning  of  her  egress  from  his  western 
limb:  but  at  the  same  instant  of  time,  as  seen  from  the  Ganges, 
which  is  then  at  g,  she  will  be  quite  clear  of  the  Sun  toward 
the  west;  being  then  seen  from  g  in  the  right  line  geL,  which 
makes  an  angle,  as  UeL  (equal  to  the  opposite  angle  Ceg), 
with  the  right  line  CeU :  and  this  is  the  angle  of  Venus's 


of  the  Planets  from  the  Sun.  487 

a  degree ;  and  by  this  space  of  time,  the  duration 
of  this  eclipse  caused  by  Venus  will,  on  account 
of  the  parallax,  be  shortened.  And  from  this 
shortening  of  the  time  only,  we  might  safely  enough 
draw  a  conclusion  concerning  the  parallax  which 
we  are  in  search  of,  provided  the  diameter  of  the 
Sun,  and  the  latitude  of  Venus,  were  accurately 
known.  But  we  cannot  expect  an  exact  computa- 
tion in  a  matter  of  such  subtilty. 

We  must  endeavour  therefore  to  obtain,  if  pos- 
sible, another  observation,  to  be  taken  in  those 
places  where  Venus  will  be  in  the  middle  of  the 
Sun's  disc  at  midnight;  that  is,  in  places  under 
the  opposite  meridian  to  the  former,  or  about  6 
hours  or  90  degrees  west  of  London ;  and  where 
Venus  enters  upon  the  Sun  a  little  before  its  set- 


parallax  from  the  Sun,  as  seen  from  the  Ganges  at  $•,  when  she  5s 
but  just  beginning  to  leave  the  Sun  at  {/,  as  seen  from  the  Earth's 
centre  C. 

Here  it  is  plain,  that  the  duration  of  the  transit  about  the  mouth 
of  the  Ganges  (and  also  in  the  neighbouring  places)  will  be  dimi- 
nished by  about  double  the  quantity  of  Vemis's  parallax  from  the 
Sun  at  the  beginning  and  ending  of  the  transit.  For  Venus  must  be 
at  E  in  her  orbit  when  she  is  wholly  upon  the  Sun  at  T,  as  seen 
from  the  Earth's  centre  C:  but  at  that  time  she  is  short  of  the  Sun, 
as  seen  from  the  Ganges  at  G,  by  the  whole  quantity  of  her  eastern 
parallax  from  the  Sun  at  that  time,  which  is  the  angle  KET.  [This 
angle,  in  fact,  is  only  23" ;  though  it  is  represented  much  larger  in 
the  figure,  because  the  Earth  therein  is  a  vast  deal  too  big.]  Now, 
as  Venus  moves  at  the  rate  of  4'  in  an  hour,  she  will  move  23"  in  5 
minutes  45  seconds :  and  therefore,  the  transit  will  begin  later  by  5 
minutes  45  seconds  at  the  banks  of  the  Ganges  than  at  the  Earth's 
centre. — When  the  transit  is  ending  at  £7,  as  seen  from  the  Earth's 
centre  at  C,  Venus  will  be  quite  clear  of  the  Sun  (by  the  whole 
quantity  of  her  western  parallax  from  him)  as  seen  from  the  Ganges, 
which  is  then  at  g :  and  this  parallax  will  be  22",  equal  to  the  space 
through  which  Venus  moves  in  5  minutes  30  seconds  of  time :  so 
that  the  transit  will  end  5.|  minutes  sooner  as  seen  from  the  Ganges^ 
than  as  seen  from  the  Earth's  centre. 

Here  the  whole  contraction  of  the  duration  of  the  transit  at  the 
mouth  of  the  Ganges  will  be  31  minutes  15  seconds  of  time:  for  it 
is  5  minutes  45  seconds  at  the  beginning,  and  5  minutes  30  seconds 
at  the  end. 

SO. 


468  The  Method  of  finding  the  Distances 

ting,  and  goes  off  a.  little  after  its  rising.  And 
this  will 'happen  under  the  above-mentioned  meri- 
dian, and  where  the  elevation  of  the  north  pole  is 
about  56  degrees;  that  is,  in  a  part  of  Hudson's 
Bay,  near  a  place  called  Port-Nelson.  For,  in  this 
and  the  adjacent  places,  the  parallax  of  Venus  will 
increase  ths  duration  of  the  transit  by  at  least  six 
minutes  of  time;  because,  while  the  Sun,  from 
its  setting  to  its  rising,  seems  to  pass  under  the  pole, 
those  places  on  the  Earth's  disc  will  be  carried  with 
a  motion  from  east  to  west,  contrary  to  the  motion 
of  the  Ganges ;  that  is,  with  a  motion  conspiring 
with  the  motion  of  Venus ;  and  therefore  Venus 
will  seem  to  move  more  slowly  on  the  Sun,  and  to 
be  longer  in  passing  over  his  disc.* 


*  In  Fig.  I.  of  Plate  XV.  let  aCbe  the  meridian  of  the  eastern 
mouth  of  the  Ganges;  and  AC"  ;he  meridian  of  Port-Nelson  at  the 
mouth  of  York  River  in  Hudson's  Bay,  56°  north  latitude.  As 
the  meridian  of  the  Ganges  revolves  from  a  to  c,  the  meridian  of 
Port-Nelson  will  revolve  from  b  to  d;  therefore,  while  the  Ganges 
revolves  from  G  to  g,  through  the  arc  G?ng,  Port-Nelson  revolves 
the  contrary  way  (as  seen  from  the  Sun  or  Venus)  from  P  to  fi 

through  the  arcjptt/?. —Now,  as  the  motion  of  Venus  is  from  £ 

to  e  in  her  orbit,  while  she  seems  to  pass  over  the  Sun's  disc  in  the 
right  line  TtU,  as  seen  from  the  Earth's  centre  C,  it  is  plain  that 
tv  Idle  the  motion  of  the  Ganges  is  contrary  to  the  motion  of  Venus 
in  her  orbit,  and  thereby  shortens  the  duration  of  the  transit  at  that 
place,  the  motion  of  Port-Ntlson  is  the  same  way  as  the  motion  of 
Venus,  and  will  therefore  increase  the  duration  cf  the  transit : 
which  may  in  some  degree  be  illustrated  by  supposing,  that  while 
a  ship  is  under  sail,  if  two  birds  fly  i.long  the  bide  of  the  ship  in  con- 
trary directions  to  each  other,  the  bird  which  flies  contrary  to  the 
motion  of  the  ship  will  pass  by  it  sooner  than  the  bird  will,  which 
flies  the  same  way  that  the  ship  moves. 

In  fine,  it  is  plain  by  the  figure,  that  the  duration  of  the  transit 
must  be  longer  as  seen  from  Port-Nelson,  th^n  as  seen  from  the 
Earth's  centre ;  and  longer  as  seen  tr< :-m  the  Earth's  centre,  than 

as  seen  from  the  mouth  of  the  Ganges F<  r  Port-Ntlaon  must 

be  at  P,  and  Venus  at  A* in  her  orbit,  wh>n  she  Appears  wholly  with- 
in the  Sun  at  T:  and  the  san;e  place  must  be  at/2,  and  Venus  at  n, 
when  she  appears  at  U  beginning  to  leave  the  Sun. — The  Ganges 
must  ue  at  G,  and  Venus  at  R,  when  she  is  seen  from  G  upon 


of  the  Planets  from  the  Sun.  489 

If  therefore  it  should  happen  that  this  transit 
should  be  properly  observed  by  skilful  persons  at 
boih  these   places,    it   is  clear,    that  its   duration 
will  be   17   minutes   longer,  as   seen  from   Port- 
Nelson,  than  as  seen  from  the  East -Indies.     Nor  is 
it  oi  much  consequence  (if  the  English  shall  at  that 
time  give  any  attention  to  this  affair)  whether  the 
observation   be  made  at  Fort-George,  commonly 
called  Madras,  or  at  Bencoolen  on  the  western  shore 
of  the  island  of  Sumatra,  near  the  equator.    But 
if  the  French  should  be  disposed  to  take  any  pains 
herein,  an  observer  may  station  himself  convenient- 
ly enough  at  Pondicherry  on  the  \vest  shore  of  the 
bay  oi  Bengal,  where  the  altitude   of  the  pole  is 
about  12  degrees.    As  to  the  Dittch,  their  cele- 
brated mart  at  Batavia  will  afford  them  a  place  of 
observation  fit  enough  for  this  purpose,  provided 
they  also  have  but  a  disposition  to  assist  in  advanc- 
ing, in  this  particular,  the  knowledge  of  the  hea- 
vens.-— And  indeed  I  could  wish  that  many  obser- 
vations of  the  same  phenomenon  might  be  taken  by 
different  persons  at   several  places,   both   that   we 
might  arrive   at  a  greater  degree  of  certainty  by 
their  agreement,  and  also  lest  any  single  observer 
should  be  deprived,  by  the  intervention  of  clouds, 
of  a  sight,  which  I  know  not  whether  any  man  liv- 
ing in  this  or  the  next  age  will  ever  see  again  ;  and 
on  which  depends  the  certain  and  adequate  solution 
of  a  problem  the  most  noble,  and  at  any  other  time 
not  to  be  attained  to.     I  recommend  it,  therefore, 
again  and  again,    to    those    curious  astronomers, 
who  (when  I  am  dead)  will  have  an  opportunity 
of  observing  these  things,  that  they  would  remem- 

the  Sun  at  T;  and  the  same  place  must  be  at  £,  and  Venus  at  r, 
when  she  begins  to  leave  the  Sun  at  (7,  as  seen  from  g.  So  that 
Venus  must  move  from  JV  to  n  in  her  orbit,  while  she  is  seen  to  pass 
over  the  Sun  from  Port-Nelson ;  from  E  to  e  in  passing  over  the 
Sun,  as  seen  from  the  Earth's  centre ;  and  only  from  R  to  r  while 
she  passes  over  the  Sun,  as  seen  from  the  banks  of  the  Ganges. 


49t  The  Method  of  finding  the  Distances 

her  this  my  admonition,  and  diligently  apply  them- 
selves with  all  their  might  to  the  making  of  this  ob- 
servation ;  and  I  earnestly  wish  them  all  imaginable 
success ;  in  the  first  place,  that  they  may  not,  by 
the  unseasonable  obscurity  of  a  cloudy  sky,  be  de- 
prived of  this  most  desirable  sight ;  and  then,  that 
having  ascertained  with  more  exactness  the  magni- 
tudes of  the  planetary  orbits,  it  may  redound  to  their 
immortal  fame  and  glory. 

We  have  now  shewn,  that  by  this  method  the 
Sun's  parallax  may  be  investigated  to  within  its 
five -hundredth  part,  which  doubtless  will  appear 
wonderful  to  some.  But  if  an  accurate  observation 
be  made  in  each  of  the  places  above  marked  out, 
\ve  have  already  demonstrated  that  the  durations  of 
this  eclipse  made  by  Venus  will  diifer  from  each 
other  by  17  minutes  of  time;  that  is,  upon  a  sup- 
position that  the  Sun's  parallax  is  12?".  But  if 
the  difference  shall  be  found  by  observation  to  be 
greater  or  less,  the  Sun's  parallax  will  be  greater 
or  less,  nearly  in  the  same  proportion.  And  since 
17  minutes  of  time  are  answerable  to  12£  seconds 
of  solar  parallax,  for  every  second  of  parallax  there 
will  arise  a  difference  of  more  than  80  seconds  of 
time ;  whence,  if  we  have  this  difference  true  to 
two  seconds,  it  will  be  certain  what  the  Sun's  pa- 
rallax is  to  within  a  40th  part  of  one  second;  and 
therefore  his  distance  will  be  determined  to  within 
its  500dth  part  at  least,  if  the  parallax  be  not  found 
less  than  what  we  have  supposed :  for  40  times  12$ 
make  500. 

And  now  I  think  I  have  explained  this  matter 
fully,  and  even  more  than  I  needed  to  have  done, 
to  those  who  understand  astronomy ;  and  I  would 
have  them  take  notice,  that  on  this  occasion,  I 
have  had  no  regard  to  the  latitude  of  Venus,  both 
to  avoid  the  inconvenience  of  a  more  intricate  cal- 
culation, which  would  render  the  conclusion  less 
evident ;  and  also  because  the  motion  of  the  nodes 


of  the  Planets  from  the  Sun.  491 

of  Venus  is  not  yet  discovered,  nor  can  be  deter- 
mined  but  by  such  conjunctions  of  the  planet  with 
the  Sun  as  this  is.  For  we  conclude  that  Venus 
will  pass  4  minutes  below  the  Sun's  centre,  only 
in  consequence  of  the  supposition  that  the  plane 
of  Venus 's  orbit  is  immoveable  in  the  sphere  of 
the  fixed  stars,  and  that  its  nodes  remain  in  the 
same  places  where  they  were  found  in  the  year 
1639.  But  if  Venus  in  the  year  1761,  should 
move  over  the  Sun  in  a  path  more  to  the  south, 
it  will  be  manifest  that  her  nodes  have  moved  back- 
ward among  the  fixed  stars ;  and  if  more  to  the 
north,  that  they  have  moved  forward ;  and  that  at 
the  rate  of  5-J  minutes  of  a  degree  in  100  Julian 
years,  for  every  minute  that  Venus's  path  shall  be 
more  or  less  distant  than  the  above-said  4  minutes 
from  the  Sun's  centre.  And  the  difference  be- 
tween  the  duration  of  these  eclipses  will  be  some^ 
what  less  than  17  minutes  of  time,  on  account  of 
Venus's  south  latitude ;  but  greater,  if  by  the  mo- 
tion of  the  nodes  forward  she  should  pass  on  the 
north  of  the  Sun's  centre. 

But  for  the  sake  of  those  who,  though  they  are 
delighted  with  sidereal  observations,  may  not  yet 
have  made  themselves  acquainted  with  the  doctrine 
of  parallaxes,  I  choose  to  explain  the  thing  a  little 
more  fully  by  a  scheme,  and  also  by  a  calculation 
somewhat  more  accurate. 

Let  us  suppose  that  at  London,  in  the  year  1761, 
on  the  6th  of  June,  at  55  minutos  after  V  in  the 
morning,  the  Sun  will  be  in  Gemini  15°  .37',  and 
therefore  that  at  its  centre  the  ecliptic  is  inclined 
toward  the  north,  in  an  angle  of  6°  10' ;  and  that 
the  visible  path  of  Venus  on  the  Sun's  disc  at  that 
time  declines  to  the  south,  making  an  angle  with 
the  ecliptic  of  8°  28' :  then  the  path  of  Venus  will 
also  be  inclined  to  the  south,  with  respect  to  the 
equator,  intersecting  the  parallels  of  declination  at 


492  The  Method  of  finding  the  Distances 

an  angle  of  2°  18'*,  Let  us  also  suppose,  that  Ve- 
nus, at  the  fore  mentioned  time,  ^  ill  be  at  her  least 
distance  from  the  Sun's  centre,  viz.  only  four  mi- 
nutes to  the  south ;  and  that  every  hour  she  will 
describe  a  space  of  4  minutes  on  the  Sun,  with  a 
retrograde  motion.  The  Sun's  semidiameter  will 
be  15'  51"  nearly,  and  that  of  Venus  37|".  And 
let  us  suppose,  for  trial's  sake,  that  the  difference  of 
the  horizontal  parallaxes  of  Venus  with  the  Sun 
(which  we  want)  is  31",  such  as  it  comes  out  if  the 
Sun's  parallax  be  supposed  12i".  Then,  on  the 
centre  C( Plate  XV  Fig.  2.)  let  the  little  circle  AB, 
representing  the  Earth's  disc,  be  described,  and  let 
his  semidiameter  CB  be  31";  and  let  the  ecliptic 
parallels  of  22  and  56  degrees  of  north  latitude  (for 
the  Ganges  and  Port-kelson]  be  drawn  within  it,  in 
the  manner  now  used  by  Astronomers  for  construct- 
ing solar  eclipses.  Let  BCg  be  the  meridian  in 
which  the  Sun  is,  and  to  this,  let  the  right  line  FHG 
representing  the  path  of  Venus  be  inclined  at  an  an- 
gle of  2°  18' ;  and  let  it  be  distant  from  the  centre 
C240  such  parts,  whereof  CB  is  31.  From  Clet 
fall  the  right  line  CH>  perpendicular  to  FG ;  and 
suppose  Venus  to  be  at  H  at  55  minutes  after  V  in 
the  morning.  Let  the  right  line  FHG  be  divided 
into  the  horary  space  III  IV,  IV  V,  V  VI,  &c.  each 
equal  to  CH;  that  is,  to  4  minutes  of  a  degree. 
Also,  let  the  right  line  LM  be  equal  to  the  diffe- 

*  This  was  an  oversight  in  the  Doctor,  occasioned  by  his  placing 
both  the  Earth's  axis  BCg  (Fig.  2.  of  Plate  XV.)  and  the  axis  of 
Venus's  orbit  C7/on  the  same  side  of  the  axis  of  the  ecliptic  CK; 
the  former  making  an  angle  of  6e  10'  therewith,  and  the  latter  an 
angle  of  8g  28';  the  difference  of  which  angles  is  only  2°  18'.  But 
the  truth  is,  that  the  Earth's  axis,  and  the  axis  of  Venus's  orbit,  will 
then  lie  on  different  sides  of  the  axis  of  the  ecliptic,  the  former  mak- 
ing an  angle  of  6°  therewith,  and  the  latter  an  angle  of  8 1°.  There- 
fore, the  sum  of  these  angles,  which  is  141°  (and  not  their  "difference 
2**  18'),  is  the  inclination  of  Venus's2 visible  path  to  the  equator 
and  parallels  of  declination. 


of  the  Planets  from  the  San.  493 

rence  of  the  apparent  semidiametcrs  of  the  Sun  and 
Venus,  which  is  15'  13i";  and  a  circle  being  de- 
scribed with  the  radius  LM,  on  a  centre  taken  in 
any  point  within  the  little  circle  AB  representing  the 
Earth's  disc,  will  meet  the  right  line  FG  in  a  point 
denoting  the  time  at  London  when  Venus  shall  touch 
the  Sun's  limb  internally,  as  seen  from  the  place  of 
the  Earth's  surface  that  answers  to  the  point  assum- 
ed in  the  Earth's  disc.  And  if  a  circle  be  describ- 
ed on  the  centre  C,  with  the  radius  LM,  it  will  meet 
the  right  line  FG>  in  the  points  F  and  G  ;  and  the,- 
spaces  FH  and  GH  will  be  each  equal  to  14'  4", 
which  space  Venus  will  appear  to  pass  over  in  3 
hours  40  minutes  of  time  at  London ;  therefore  F 
will  fall  in  II  hours  15  minutes,  and  G  in  IX  hours 
35  minutes  in  the  morning.  Whence  it  is  manifest 
that  if  the  magnitude  of  the  Earth,  on  account  of  its 
immense  distance,  should  vanish  as  it  were  into  a 
point ;  or  if,  being  deprived  of  a  diurnal  motion,  it 
should  always  have  the  Sun  vertical  to  the  same 
point  C;  the  whole  duration  of  this  eclipse  would 
be  7  hours  20  minutes.  But  the  Earth  in  that  time 
being  whirled  through  1 10  degrees  of  longitude,  with 
a  motion  contrary  to  the  motion  of  Venus,  and  con- 
sequently the  abovementioned  duration  being  con- 
tracted, suppose  12  minutes,  it  will  come  out  7 
hours  8  minutes,  or  107  degrees  nearly. 

Now  Venus  will  be  at  //,  at  her  least  distance 
from  the  Sun's  centre,  when  in  the  meridian  of  the 
eastern  mouth  of  the  Ganges,  where  the  altitude  of 
the  pole  is  about  22  degrees.  The  Sun  therefore 
w  ill  be  equally  distant  from  the  meridian  of  that 
place,  at  the  moments  of  the  ingress  and  egress  of 
the  planet,  viz.  53  *.  degrees ;  as  the  points  a  and  b 
(representing  that  place  in  the  Earth's  disc  AB)  are, 
in  the  greater  parallel,  from  the  meridian  BCg.  But 
the  diameter  efof  that  parallel  will  be  to  the  distance 
ab,  as  the  square  of  the  radius  to  the  rectangle  under 
the  sines  of  53  J  and  68  degrees;  that  is,  of  1'  2"  fc 


494  The  Method  of  finding  the  Distances 

46"  13'".  And  by  a  good  calculation  (which,  that 
I  may  not  tire  the  reader,  it  is  better  to  omit)  I  find 
that  a  circle  described  on  a  as  a  centre,  with  the  ra- 
dius LM,  will  meet  the  right  line  FH'm  the  point 
M,  at  II  hours  20  minutes  40  seconds;  but  that  be- 
ing described  round  b  as  a  centre,  it  will  meet  HG 
in  the  point  A' at  IX  hours  29  minutes  22  seconds, 
according  to  the  time  reckoned  at  London:  and 
therefore,  Venus  will  be  seen  entirely  within  the  Sun 
at  the  banks  of  the  Ganges  for  7  hours  8  minutes 
42  seconds  :  we  have  then  rightly  supposed  that  the 
duration  will  be  7  hours  8  minutes,  since  the  part  of 
a  minute  here  is  of  no  consequence. 

But  adapting  the  calculation  to  Port-Nelson,  I 
find,  that  the  Sun  being  about  to  set,  Venus  will 
enter  his  disc ;  and  immediately  after  his  rising  she 
will  leave  the  same.  That  place  is  carried  in  the 
intermediate  time  through  the  hemisphere  opposite 
to  the  Sun,  from  c  to  d,  with  a  motion  conspiring 
with  the  motion  of  Venus ;  and  therefore,  the  stay 
of  Venus  on  the  Sun  will  be  about  4  minutes 
longer,  on  account  of  the  parallax ;  so  that  it  will 
be  at  least  7  hours  24  minutes,  or  111  degrees  of 
the  equator.  And  since  the  latitude  of  the  place 
is  56  degrees,  as  the  square  of  the  radius  is  to  the 
rectangle  contained  under  the  sines  55£  and  34 
degrees,  so  is  AB,  which  is  1'  2",  to  cd,  which  is 
28"  33'".  And  if  the  calculation  be  justly  made, 
it  will  appear  that  a  circle  described  on  c  as  a  cen- 
tre, with  the  radius  LM>  will  meet  the  right  line 
FH'm  O  at  II  hours  12  minutes  45  seconds;  and 
that  such  a  circle  described  on  d  as  a  centre, 
will  meet  HG  in  P,  at  IX  hours  36  minutes  37 
seconds ;  and  therefore  the  duration  at  Port -Nelson 
will  be  7  hours  23  minutes  52  seconds,  which  is 
greater  than  at  the  mouth  of  the  Ganges  by  15 
minutes  10  seconds  of  time.  But  if  Venus  should 
pass  over  the  Sun  without  having  any  latitude,  the 
difference  would  be  18  minutes  40  seconds;  and 


of  the  Planets  from  the  Sun.  495 

if  she  should  pass  4'  north  of  the  Sun's  centre,  the 
difference  would  amount  to  21  minutes  40  seconds, 
and  will  be  still  greater,  if  the  planet's  north  latitude 
be  more  increased. 

From  the  foregoing  hypothesis  it  follows,  that  at 
London,  wfren  the  Sun  rises,  Venus  will  have  enter- 
ed his  disc;  and  that,  at  IX  hours  37  minutes  in  the 
morning,  she  will  touch  the  limb  of  the  Sun  inter- 
nally at  going  off;  and  lastly,  that  she  will  not  en- 
tirely leave  the  Sun  till  IX  hours  56  minutes. 

It  likewise  follows  from  the  same  hypothesis,  that 
the  centre  of  Venus  should  just  touch  the  Sun's 
northern  limb  in  the  year  1769",  on  the  third  of  June, 
at  XI  o'clock  at  night.  So  that,  on  account  of  the 
parallax,  it  will  appear  in  the  northern  parts  of  Nor- 
way, entirely  within  the  Sun,  which  then  does  not  set 
to  those  parts ;  while,  on  the  coasts  of  Peru  and 
Chili,  it  will  seem  to  travel  over  a  small  portion  of 
the  disc  of  the  setting  Sun ;  and  over  that  of  the 
rising  Sun  at  the  Molucca  Islands,  and  in  their  neigh- 
bourhood.— But  if  the  nodes  of  Venus  be  found  to 
have  a  retrograde  motion  (as  there  is  some  reason  to 
believe  from  some  later  observations  they  havej,  then 
Venus  will  be  seen  every  where  within  the  Sun's 
disc ;  and  will  afford  a  much  better  method  for  find- 
ing the  Sun's  parallax,  by  almost  the  greatest  dif- 
ference in  the  duration  of  these  eclipses  that  can  pos- 
sibly happen. 

But  how  this  parallax  may  be  deduced  from  ob- 
servations made  somewhere  in  the  East  Indies,  in 
the  year  1761,  both  of  the  ingress  and  egress  of 
Venus,  and  compared  with  those  made  in  its  going 
off  with  us,  namely,  by  applying  the  angles  of  a 
triangle  given  in  specie  to  the  circumference  of  three 
equal  circles,  shall  be  explained  on  some  other  oc- 
casion. 

3R 


496  The  Method  of  finding  the  Distances 


ARTICLE  IV. 

Showing  that  the  whole  method  proposed  by  the  Doc- 
tor cannot  be  put  in  practice,  and  why. 

27.  In  the  above  Dissertation,  the  Doctor  has  ex- 
plained his  method  with  great  modesty,  and  even 
with  some  doubtfulness  with  regard  to  its  full  suc- 
cess.    For  he  tells  us,  that  by  means  of  this  transit 
the  Sun's  parallax  may  only  be  determined  within 
its  five  hundredth  part,  provided  it  be  not  less  than 
12j";  that  there  may  be  a  good  observation  made 
at  Port-Nelson,  as  well  as  about  the  banks  of  the 
Ganges  ;  and  that  Venus  does  not  pass  more  than  4 
minutes  of  a  degree  below  the  centre  of  the  Sun's 
disc. — He  has  taken  all  proper  pains  not  to  raise  our 
expectations  too  high,  and  yet,  from  his  well-known 
abilities,  and  character  as  a  great  astronomer,  it  seems 
mankind  in  general  have  laid  greater  stress  upon  his 
method,  than  he  ever  desired  them  to  do.    Only,  as 
he  wSs  convinced  it  was  the  best  method  by  which 
this  important  problem  can  ever  be  solved,  he  re- 
commended it  warmly  for  that  reason.     He  had  not 
then  made  a  sufficient  number  of  observations,  by 
which  he  could  determine,  with  certainty,  whether 
the  nodes  of  Venus's  orbit  have  any  motion ;  or  if 
they  have,  whether  it  be  backward  or  forward  with 
respect  to  the  stars.    And  consequently,  having  not 
then  made  his  own  tables,  he  was  obliged  to  calcu- 
late from  the  best  that  he  could  find.    But  those  ta- 
bles allow  of  no  motion  to  Venus's  nodes,  and  also 
reckon  her  conjunction  with  the  Sun  to  be  about 
half  an  hour  too  late. 

28.  But  more  modern  observations  prove,  that 
the  nodes  of  Venus's  orbit  have  a  motion  back- 
ward, or  contrary  to  the  order  of  the  signs,  with 
respect  to  the  fixed  stars.     And  this  motion  is  al- 
lowed for  in  the  Doctor's  tables,    a  great  part  oi 
which  were  made  from  his  own  observations.    And 


of  the  Planets  from  the  Sun.  497 

it  appears  by  these  tables,  that  Venus  will  be  so 
much  farther  past  her  descending  node  at  the  time  of 
this  transit,  than  she  was  past  her  ascending  node  at 
her  transit,  in  November  1639;  that  instead  of  pas- 
sing only  four  minutes  of  a  degree  below  the  Sun's 
centre  in  this,  she  will  pass  almost  10  minutes  of  a 
degree  below  it :  on  which  account,  the  line  of  her 
transit  will  be  so  much  shortened,  as  will  make  her 
passage  over  the  Sun's  disc  about  an  hour  and  20 
minutes  less  than  if  she  passed  only  4  minutes  below 
the  Sun's  centre  at  the  middle  of  her  transit.  And 
therefore,  her  parallax  from  the  Sun  will  be  so  mucl^ 
diminished,  both  at  the  beginning  and  end  of  her 
transit,  and  at  all  places  from  which  the  whole  of  it 
will  be  seen,  that  the  difference  of  its  durations,  as 
seen  from  them,  and  as  supposed  to  be  seen  from 
the  Earth's  centre,  will  not  amount  to  11  minutes  of 
time. 

29.  But  this  is  not  all ;  for  although  the  transit 
will  begin  before  the  Sun  sets  to  Port-Nelson,  it  will 
be  quite  over  before  he  rises  to  that  place  next  morn- 
ing, on  account  of  its  ending  so  much  sooner  than 
as  given  by  the  tables  to  which  the  Doctor  was  oblig- 
ed to  trust.     So  that  we  are  quite  deprived  of  the 
advantage  that  otherwise  would  have  arisen  from  ob- 
servations made  at  Port-Nelson. 

30.  In  order  to  trace  this  affair  through  all  its 
intricacies,  and  to  render  it  as  intelligible  to  the  rea- 
der as  I  can,  there  will  be  an  unavoidable  necessity 
of  dwelling  much  longer  upon  it  than  I  could  other- 
wise wish.     And  as  it  is  impossible  to  lay  down 
truly  the  parallels  of  latitude,  and  the  situations  of 
places  at  particular  times,  in  such  a  small  disc  of  the 
Earth  as  must  be  projected  in  such  a  sort  of  diagram 
as  the  Doctor  has  given,  so  as  to  measure  thereby 
the  exact  times  of  the  beginning  and  ending  of  the 
transit  at  any  given  place,  unless  the  Sun's  disc  be 
made  at  least  30  inches  diameter  in  the  projection, 
and  to  which  the  Doctor  did  not  quite  trust  without 
making  some  calculations ;  I  shall  take  a  different 


498  The  Method  of  jindmg  the  Distances 

method,  in  which  the  Earth's  disc  may  be  made  as 
large  as  the  operator  pleases:  but  if  he  makes  it  only 
6  inches  in  diameter,  he  may  measure  the  quantity 
of  Venus's  parallax  from  the  Sun  upon  it,  both  in 
longitude  and  latitude,  to  the  fourth  part  of  a  second, 
for  any  given  time  and  place  ;  and  then,  by  an  easy 
calculation  in  the  common  rule  of  three,  he  may  find 
the  effect  of  the  parallaxes  on  the  duration  of  the 
transit.  In  this  I  shall  first  suppose  with  the  Doc- 
tor, that  the  Sun's  horizontal  parallax  is  12-j" ;  and 
consequently,  that  Venus's  horizontal  parallax  from 
the  Sun  is  31".  And  after  projecting  the  transit,  so 
as  to  find  the  total  effect  of  the  parallax  upon  its  du- 
ration, I  shall  next  show  how  nearly  the  Sun's  real 
parallax  may  be  found  from  the  observed  intervals 
between  the  times  of  Venus's  egress  from  the  Sun, 
at  particular  places  of  the  earth ;  which  is  the  method 
now  taken  both  by  the  English  and  French  astro- 
nomers, and  is  a  surer  way  whereby  to  come  at  the 
real  quantity  of  the  Sun's  parallax,  than  by  observ- 
ing how  much  the  whole  contraction  of  duration 
of  the  transit  is,  either  at  Bencoolen^  Batavia,  or 
Pondicherry. 


ARTICLE  V. 

Showing  how  to  project  the  transit  of  Venus  on  the  Sun's 
disc,  as  seen  from  different  places  of  the  Earth;  so  as 
tojindwhat  its  visible  duration  must  be  at  any  given 
place,  according  to  any  assumed  parallax  of  the  Sun; 
and  from  the  observed  intervals  between  the  times  of 
Venus*  s  egress  from  the  Sun  at  particular  places ,  to  find 
the  Surfs  true  horizontal  parallax. 

31.  The  elements  for  this  projection  are  as  fol- 
lows : 

I.  The  true  time  of  conjunction  of  the  Sun  and 
Venus ;  which,  as  seen  from  the  Earth's  centre, 
and  reckoned  according  to  the  equal  time  at 


of  the  Planets  from  the  Sun.  499 

London,  is  on  the  6th  of  June  1761,  at  46  mi- 
nutes 17  seconds  after  V  in  the  morning,  accord- 
ing to  Dr.  H ALLEY'S  tables. 

II.  The  geocentric  latitude  of  Venus  at  that  time, 
9'  43"  south. 

III.  The  Sun's  semidiameter,  15'  50". 

IV.  The  semidiameter  of  Venus  (from  the  Doctor's 
Dissertation),  37|". 

V.  The  difference  of  the  semidiameters  of  the  Sun 
and  Venus,   15'  1^". 

VI.  Their  sum,   16'  *7j". 

VII.  The  visible  angle  which  the  transit-line  makes 
with  the  ecliptic  8°  31';  the  angular  point  (or 
descending  node)  being  1°  6'  18"  eastward  from 
the  Sun,  as  seen  irom  the  Earth ;  the  descending 
node  being  in  t   14°  29'  37",  as  seen  from  the 
Sun;  and  the  Sun  in  n  15°  35'  55",  as  seen  from 
the  Earth. 

VIII.  The  angle  which  the  axis  of  Venus's  visible 
path  makes  with  the  axis  of  the  ecliptic,  8°  31' ; 
the  southern  half  of  that  axis  being  on  the  left 
hand  (or  eastward)  of  the  axis  of  the  ecliptic,  as 
seen  from  the  northern  hemisphere  of  the  Earth, 
which  would  be  to  the  right  hand,  as  seen  from 
the  Sun. 

IX.  The  angle  which  the  Earth's  axis  makes  with 
the  axis  of  the  ecliptic,  as  seen  from  the  Sun, 
6°;  the  southern  half  of  the  Earth's  axis  lying  to 
the  right  hand  of  the  axis  of  the  ecliptic,  in  the 
projection  which  would  be  to  the  left  hand,  as 
seen  from  the  Sun. 

X.  The  angle  which  the  Earth's  axis  makes  with 
the  axis  of  Venus's  visible  path,  14°  31';  viz. 
the  Sum  of  No.  VIII.  and  IX. 

XL  The  true  motion  of  Venus  on  the  Sun,  given 
by  the  tables  as  if  it  were  seen  from  the  Earth's 
centre,  4  minutes  of  a  degree  in  60  minutes  of 
time. 


500  The  Method  of  finding  the  Distance* 

32.  These  elements  being  collected,  make  a  scale 
of  any  convenient  length,  as  that  of  Fig.  1.  in  Plate 
XVI,  and  divide  it  into  17  equal  parts,  each  of  which 
shall  be  taken  for  a  minire  of  a  degree,  then  divide 
the  minute  next  to  the  left  hand  into  60  equal  p^rts 
for  seconds,    by  diagonal   lines,  as  in  the  figure. 
The  reason  for  dividing  the  scale  into  17  parts  or 
minutes  is,  because  the  sum  of  the  semidiameters 
of  the  Sun  and  Venus  exceeds  16  minutes  of  a  de- 
gree.    See  No.  VI. 

33.  Draw  the  right  line^QS  (Fig.  2.)  for  a  small 
part  of  the  ecliptic,  and  perpendicular  to  it  draw  the 
right  line  CvE  for  the  axis  of  the  ecliptic  on  the 
southern  half  of  the  Sun's  disc. 

34.  Take  the  Sun's  semidiameter,  15'  50"  from 
the  scale  with  your  compasses ;  and  with  that  ex- 
tent, as  a  radius,  set  one  foot  in  C  as  a  centre,  and 
describe  the  semicircle  AEG  for  the  southern  half 
of  the  Sun's  disc ;  because  the  transit  is  on  that  half 
of  the  Sun. 

35.  Take  the  geocentric  latitude  of  Venus,  9' 
43",  from  the  scale  with  your  compasses ;  and  set 
that  extent  from  C  to  v,  on  the  axis  of  the  ecliptic : 
and  the  point  v  shall  be  the  place  of  Venus's  centre 
on  the  Sun,  at  the  tabular  moment  of  her  conjunc- 
tion with  the  Sun. 

36.  Draw  the  right  line  CBD,  making  an  angle 
of  8°  31'  with  the  axis  of  the  ecliptic,  toward  the 
left  hand ;  and  this  line  shall  represent  the  axis  of 
Venus's  geocentric  visible  path  on  the  Sun. 

37.  Through  the  point  of  the  conjunction  v,  in 
the  axis  of  the  ecliptic,  draw  the  right  line  qtr  for 
the  geocentric  visible  path  of  Venus  over  the  Sun's 
disc,  at  right  angles  to  CBJD,  the  axis  of  her  orbit, 
which  axis  will  divide  the  line  of  her  path  into  two 
equal  parts  qt  and  tr. 

38.  Take  Venus's  horary  motion  on  the  Sun, 
4'  from  the  scale  with  your  compasses;  and  with 
that  extent  make  marks  along  the  transit-line  qtr. 
The  equal  spaces,  from  mark  to  mark,  show  how 


of  the  Planets  from  the  Sun.  501 

much  of  that  line  \  enus  moves  through  in  each 
huur,  as  seen  from  the  Earth's  centre,  during  her 
continuance  on  the  Sun's  disc. 

39.  Divide  each   of  these  horary  spaces,  from 
mark  to  mark,  into  60  equal  parts  for  minutes  of 
time;  and  set  the  hours  to  the  proper  marks  in  such 
a  manner,  that  the  true  time  ot  conjunction  of  the 
Sun  and  Venus,  46|  minutes  after  V  in  the  morn- 
ing, may  fall  into  the  point  v,  where  the  transit-line 
cuts  the  axis  of  the  ecliptic,     bo  the  point  v  shall 
denote  the  place  of  Venus's  centre  on  the  Sun,  at 
the  instant  of  her  ecliptical  conjunction  with  the  Sun, 
and  t  (in  the  axis  CtD  of  her  orbit)  w  ill  be  the  mid- 
dle of  her  transit ;  which  is  at  24  minutes  after  V  in 
the  morning,  as  seen  from  the  Earth's  centre,  and 
reckoned  by  the  equal  time  at  London. 

40.  Take  the  difference  of  the  semidiameters  of 
the  Sun  and  Venus,   15'  l^J",  in  your  compasses 
from  the  scale ;  and  with  that  extent,  setting  one  foot 
in  the  Sun's  centre  C,  describe  the  arcs  A*  and  T 
w  ith  the  other  crossing  the  transit- line  in  the  points 
k  and  /;  which  are  the  points  on  the  Sun's  disc  that 
are  hid  by  the  centre  of  Venus  at  the  moments  of  her 
two  internal  contacts  with  the  Sun's  limb  or  edge, 
at  J/and  N ':  the  former  of  these  is  the  moment  of 
Venus's  total  ingress  on  the  Sun,  as  seen  from  the 
Earth's  centre,  w7hich  is  at  28  minutes  after  II  in 
the  morning,  as  reckoned  at  London  ;  and  the  latter 
is  the  moment  wrhen  her  egress  from  the  Sun  begins, 
as  seen  from  the  Earth's  centre,  which  is  20  minutes 
after  VIII  in  the  morning  at  London.    The  interval 
between  these  two  contacts  is  5  hours  52  minutes. 

41.  The  central  ingr-ess  of  Venus  on  the  Sun  is 
the  moment  when  htr  centre  is  on  the  Sun's  eastern 
limb  at  M,  which  is  at  15  minutes  after  two  in  the; 
morning :  and  her  central  egress  from  the  Sun  is 
the  moment  when  her  centre  is  on  the  Sun's  western 
limb  at  w ;  which  is  at  33  minutes  aftey  VIII  in 


502  The  Method  of  finding  the  Distances 

the  morning,  as  seen  from  the  Earth's  centre,  and 
reckoned  according  to  the  time  at  London.  The  in- 
terval between  these  times  is  6  hours  18  minutes. 

42.  Take  the  sum  of  the  semidiameters  of  the 
Sun  and  Venus,   16'  2/-J",  in  your  compasses  from 
the  scale ;  and  with  that  extent,  setting  one  foot  in 
the  Sun's  centre  C,  describe  the  arcs  Q  and  R  with 
the  other,  cutting  the  transit-line  in  the  points  q  arid 
r,  which  are  the  points  in  open  space  (clear  of  the 
Sun)  where  the  centre  of  Venus  is,  at  the  moments 
of  her  two  external  contacts  with  the  Sun's  limb 
at  S  and  W;  or  the  moments  of  the  beginning  and 
ending  of  the  transit  as  seen  from  the  Earth's  cen- 
tre ;  the  former  of  which  is  at  3  minutes  after  II  in 
the  morning  at  London,  and  the  latter  at  45  minutes 
after  VIIL    The  interval  between  these  moments  is 
6  hours  42  minutes. 

43.  Take  the  semidiameter  of  Venus  37-J",  in 
your  compasses  from  the  scale  :  and  with  that  ex- 
tent as  a  radius,  on  the  points  q,  k,  t,  /,  r,  as  cen- 
tres, describe  the  circles  HS,  MI,  OF,  PN,  WY, 
for  the  disc  of  Venus,  at  her  first  contact  at  S,  her 
total  ingress  at  M,  her  place  on  the  Sun  at  the  mid- 
dle of  her  transit,  her  beginning  of  egress  at  JV,  and 
her  last  contact  at  IV. 

44.  Those  who  have  a  mind  to  project  the  Earth's 
disc  on  the  Sun,  round  the  centre  C,  and  to  lay 
down  the  parallels  of  latitude  and  situations  of  places 
thereon,  according  to  Dr.  HAL  LEY'S  method,  may 
draw7  Cf  for  the  axis  of  the  Earth,  produced  to  the 
southern  edge  of  the  Sun  at/V  and  making  an  an- 
gle ECfoi'  6°  with  the  axis  of  the  ecliptic  CE  : 
but  he  will  find  it  very  difficult  and  uncertain  to 
mark  the  places  on  that  disc,   unless  he  makes  the 
Sun's  semidiameter  AC  15  inches  at  least :  other- 
wise the  line  Cf  is  of  no  use  at  all  in  this  projec- 
tion.— The  following  method  is  better. 

45.  In  Fig.  3.  of  Plate  XVI  make  the  line  AB 
of  any  convenient   length,   and  divide   it  into  31 
equal  parts,  each  of  which  may  be  taken  for  a  second 


of  the  Planets  from  the  Sun. 

of  Venus's  parallax  either  from  or  upon  the  Sun 
(her  horizontal  parallax  from  the  Sun  being  sup- 
posed to  be  31");  and  taking  the  whole  length 
AB  in  your  compasses,  set  one  foot  in  C  (Fig.  4.) 
as  a  centre,  and  describe  the  circle  AEBD  for  the 
Earth's  enlightened  disc,  whose  diameter  is  62",  or 
double  the  horizontal  parallax  of  Venus  from  the 
Sun.  In  this  disc,  draw  ACB  for  a  small  part  of 
the  ecliptic,  and  at  right  angles  to  it  draw  ECD  for 
the  axis  of  the  ecliptic.  Draw  also  NCS  both  for 
the  Earth's  axis  and  universal  solar  meridian,  mak- 
ing an  angle  of  6°  with  the  axis  of  the  ecliptic,  as 
seen  from  the  Sun  ;  HCI  for  the  axis  of  Venus's 
orbit,  making  an  angle  of  8°  31'  with  ECD,  the 
axis  of  the  ecliptic ;  and  lastly,  VCO  for  a  small 
part  of  Venus's  orbit,  at  right  angles  to  its  axis. 

46.  This  figure  represents  the  Earth's  enlightened 
disc,  as  seen  from  the  Sun  at  the  time  of  the  transit. 
The  parallels  of  latitude  of  London,  the  eastern 
mouth  of  the  Ganges^  Bencoolen,  and  the  island  of 
St.  Helena,  are  laid  down  in  it,  in  the  same  manner 
as  they  would  appear  to  an  observer  on  the  Sun,  if 
they  were  really  drawn  in  circles  on  the  Earth's  sur- 
face (like  those  on  a  common  terrestrial  globe)  and 
could  be  visible  at  such  a  distance. — The  method 
of  delineating  these  parallels  is  the  same  as  already 
described  in  the  XlXth  chapter,  for  the  construc- 
tion of  solar  eclipses. 

47.  The  points  Where  the   curve-lines   (called 
hour-circles)  XI  JV,  XJV,   &c.  cut  the  parallels  of 
latitude,  or  paths  of  the  four  places  above  mention- 
ed, are  the  points  at  which  the  places  themselves 
would  appear  in  the  disc,  as  seen  from  the  Sun,  at 
these  hours  respectively.    When  either  place  comes 
to  the  solar  meridian  NCS  by  the  Earth's  rotation 
on  its  axis,  it  is  noon  at  that  place  ;  and  the  diffe- 
rence, in  absolute  time,  between  the  noon  at  that 
place  and  the  noon  at  any  other  place,  is  in  propor- 
tion to  the   difference  of  longitude  of  these  two 
places,  reckoning  one  hour  lor  every  1.5  degrees  of 

3  S 


504  The  Method  of  finding  the  Distances 

longitude,  and  4  minutes  for  each  degree :  adding 
the  time  if  the  longitude  be  east,  but  subtracting  it 
if  the  longitude  be  west. 

48.  The  distance  of  either  of  these  places  from 
HCI  (the  axis  of  Venus's*  orbit)  at  any  hour  or 
part  of  an  hour,  being  measured  upon  the  scale  AB 
in  Fig.  3.  will  be  equal  to  the  parallax  of  Venus 
from  the  Sun  in  the  direction  of  her  path ,  and  this 
parallax,  being  always  contrary  to  the  position  of  the 
place,  is  eastward  as  long  as  the  place  keeps  on  the 
left  hand  of  the  axis  of  the  orbit  of  Venus,  as  seen 
from  the  sun  ;  and  westward  when  the  place  gets  to 
the  right  hand  of  that  axis.   So  that,  to  all  the  places 
which  are  posited  in  the  hemisphere  HVI  of  the 
disc,  at  any  given  time,  Venus  has  an  eastern  paral- 
lax ;   but  when  the  Earth's  diurnal  motion  carries 
the  same  places  into  the  hemisphere  HOI,  the  paral- 
lax of  Venus  is  westward. 

49.  When  Venus  has  a  parallax  toward  the  east, 
as  seen  from  any  given  place  on  the  Earth's  surface, 
either  at  the  time  of  her  total  ingress,  or  beginning 
of  egress,  as  seen  from  the  Earth's  centre ;  add  the 
time  answering  to  this  parallax  to  the  time  of  ingress 
or  egress  at  the  Earth's  centre,  and  the  sum  will  be 
the  time,  as  seen  from  the  given  place  on  the  Earth's 
surface  :   but  when  the  parallax  is  westward,  sub- 
tract the  time  answering  to  this  parallax  from  the 
time  of  total  ingress  or  beginning  of  egress,  as  seen 
from  the  Earth's  centre,  and  the  remainder  will  be 
the  time,  as  seen  from  the  given  place  on  the  sur- 
face, so  far  as  it  is  affected  by  this  parallax. — The 
reason  of  this  is  plain  to  every  one  who  considers, 

*  In  a  former  edition  of  this,  I  made  a  mistake,  in  taking-  the  pa- 
rallax in  longitude  instead  of  the  parallax  in  the  d'n-ection  of  the  orbit 
of  Venus ;  and  the  parallax  in  latitude  instead  of  the  parallax  in  lines 
perpendicular  to  her  orbit.  But  in  this  edition,  these  errors  are  cor- 
rected ;  which  make  some  small  differences  in  the  quantities  of  the 
parallaxes,  and  in  the  times  depending  on  them  ;  as  will  appear  by 
comparing  them  in  this  with  those  in  the  former  edition 


of  the  Planets  from  the  Sun.  505 

that  an  eastern  parallax  keeps  the  planet  back,  and 
a  western  parallax  carries  it  forward,  with  respect  to 
its  ti  ue  place  or  position,  at  any  instant  of  time,  as 
seen  from  the  Earth's  centre. 

50.  The  nearest  distance  of  any  given  place  from 
VCO^  the  plane  of  Venus's  orbit  tit  any  hour  or 
part  of  an  hour,  being  measured  on  the  scale  AB  in 
Fig.  3.  will  be  equal  to  Venus's  parallax  in  lines 
perpendicular  to  her  path  ;  which  is  northward  from 
the  true  line  of  her  path  on  the  Sun,  as  seen  from 
the  Earth's  centre,  if  the  given  place  be  on  the  south 
side  of  the  plane  of  her  orbit  J^CO  on  the  Earth's 
disc ;  and  the  contrary,  if  the  given  place  be  on  the 
north  side  of  that  plane ;  that  is,  the  parallax  is  al- 
ways contrary  to  the  situation  of  the  place  on  the 
Earth's  disc,  with  respect  to  the  plane  of  Venus's 
orbit  on  it. 

51.  As  the  line  of  Venus's  transit  is  on   the 
southern  hemisphere  of  the  Sun's  disc,  it  is  plain 
that  a  northern  parallax  will  cause  her  to  describe  a 
longer  line  on  the  Sun,  than  she  would  if  she  had  no 
such  parallax  ;  and  a  southern  parallax  will  cause  her 
to  describe  a  shorter  line  on  the  Sun,  than  if  she  had 
no  such  parallax. — And  the  longer  this  line  is,  the 
sooner  will  her  total  ingress  be,  and  the  later  will 
be  her  beginning  of  egress  ;  and  just  the  contrary, 
if  the  line  be  shorter. — But  to  all  places  situate  on 
the  north  side  of  the  plane  of  her  orbit,  in  the  hemis- 
phere VHO)  the  parallax  in  lines  perpendicular  to 
her  orbit  is  south  ;  and  to  all  places  situate  on  the 
south  side  of  the  plane  of  her  orbit,  in  the  hemis- 
phere FT09  this  parallax  is  north.     Therefore,  the 
line  of  the  transit  will  be  shorter  to  all  places  in  the 
hemisphere  7HO,  than  it  will  be,  as  seen  from  the 
Earth's  centre,  where  there  is  no  parallax ;  and  long- 
er to  all  places  in  the  hemisphere  710.    So  that  the 
time  answering  to  this  parallax  must  be  added  to  the 
time  of  total  ingress,  as  seen  from  the  Earth's  centre, 
and  subtracted  from  the  beginning  of  egress,   as 


506  The  Method  of  finding  the  Distances 

seen  from  the  Earth's  centre,  in  order  to  have  the 
true  time  of  total  ingress  and  beginning  of  egress  as 
seen  from  places  in  the  hemisphere  VHO :  and  just 
the  reverse  for  places  in  the  hemisphere  VIO. — It 
was  proper  to  mention  these  circumstances,  for  the 
reader's  more  easily  conceiving  the  reason  of  apply- 
ing the  times  answering  to  these  parallaxes  in  the 
subsequent  part  of  this  article :  for  it  is  their  sum  in 
some  cases,  and  their  difference  in  others,  which  be- 
ing applied  to  the  times  of  total  ingress  and  beginning 
of  egress  as  seen  from  the  Earth's  centre,  that  will 
give  the  times  of  these  phenomena  as  seen  from  given 
places  on  the  Earth's  surface. 

52.  The  angle  which  the  Sun's   semidiameter 
subtends,  as  seen  from  the  Earth,  at  all  times  of  the 
year,  has  been  so  well  ascertained  by  late  observa- 
tions, that  we  can  make  no  doubt  of  its  being  15'  50" 
on  the  day  of  the  transit ;   and  Venus's  latitude  has 
also  been  so  well  ascertained  at  many  different  times 
of  late,  that  we  have  very  good  reason  to  believe  it 
will  be  9'  43"  south  of  the  Sun's  centre  at  the  time 
of  her  conjunction  with  the  Sun. — If  then  her  semi- 
diameter  at  that  time  be  37^"  (as  mentioned  by  Dr. 
HALLEY)  it  appears  by  the  projection  (Fig.  2.)  that 
her  total  ingress  on  the  Sun,  as  seen  from  the  Earth's 
centre,  will  be  at  28  minutes  after  two  in  the  morn- 
ing (HO.),  and  her  beginning  of  egress  from  the  Sun 
will  be  20  minutes  after  VIII,  according  to  the  time 
reckoned  at  London. 

53.  As  the  total  ingress  will  not  be  visible  at  Lon- 
don we  shall  not  here  trouble  the  reader  about  Ve- 
nus's parallax  at  that  time. — But  by  projecting  the 
situation  of  London  on  the  Earth's  disc  (Fig.  4.)  for 
the  time  when  the  egress  begins,  we  find  it  will  then 
be  at  /,  as  seen  from  the  Sun. 

Draw  Id  parallel  to  Venus's  orbit  FCO,  and  lu 
perpendicular  to  it :  the  former  is  Venus's  eastern 
parallax  in  the  direction  of  her  path  at  the  beginning 
of  her  egress  from  the  Sun,  and  the  latter  is  her 


of  the  Planets  from  the  Sun.  507 

southern  parallax  in  a  direction  at  right  angles  to  her 
path  at  the  same  time.  Take  these  in  your  com- 
passes, and  measure  them  on  the  scale  AB  (Fig.  3.) 
and  you  will  find  the  former  parallax  to  be  10*", 
and  the  latter  211". 

54.  As  Venus's  true  motion  on  the  Sun  is  at  the 
rate  of  four  minutes  of  a  degree  in  60  minutes  of 
time  (See  No.  XI.  qf§  31.)  say,  as  4  minutes  of  a 
degree  is  to  60  minutes  of  time,  so  is  10J"  of  a  de- 
gree to  2  minutes  41  seconds  of  time  ;  which  being 
added  to  VIII  hours  20  minutes  (because  this  paral- 
lax is  eastward,  §  49.)  gives  VIII  hours  22  minutes 
41  seconds,  for  the  beginning  of  egress  at  London 
as  affected  only  by  this  parallax. — But  as  Venus  has 
a  southern  parallax  at  that  time,  her  beginning  of 
egress  will  be  sooner ;  for  this  parallax  shortens  the 
line  of  her  visible  transit  at  London. 

55.  Take  the  distance  Ct  (Fig.  2.),  or  nearest  ap- 
proach of  the  centres  of  the  Sun  and  Venus  in  your 
compasses,  and  measure  it  on  the  scale  (Fig.  1.), 
and  it  will  be  found  to  be  9'  36^" ;  and  as  the  pa- 
rallax of  Venus  from  the  Sun  in  a  direction  which 
is  at  right  angles  to  her  path  is  21|"  south,  add  it  to 
9'  361",  and  the  sum  will  be  9'  58" ;  which  is  to 
be  taken  from  the  scale  in  Fig.  1.  and  set  from  C 
to  L  in  Fig.  2.     And  then,  if  a  line  be  drawn  pa- 
rallel to  tl,  it  will  terminate  at  the  point  p  in  the  arc 
Z1,  where  Venus's  centre  will  be  at  the  beginning  of 
her  egress,  as  seen  from  London*. — But  as  her  cen- 
tre is  at  /  when  her  egress  begins  as  seen  from  the 
Earth's  centre,  take  Lp  in  your  compasses,   and 
setting  that  extent  from  t  toward  /  on  the  central 
transit-line,  you  will  find  it  to  be  5  minutes  shorter 
than  //.•  therefore  subtract  5  minutes  from  VIII  hours 
22  minutes  41  seconds,  and  there  will  remain  VIII 

*  The  reason  why  the  lines  oLp,  aBb,ct,  and  th,  which  are  the  vi- 
sible transits  at  London,  the  Ganges  mouth,  Bencoolen,  and  St.  Helena, 
are  not  parallel  to  the  central  transit-line  hi,  is  because  the  paral- 
laxes in  latitude  are  different  at  the  times  of  ingress  and  egress,  as 
seen  from  each  of  these  places.  The  method  of  drawing  these  lines 
will  be  shown  by«and-by. 


508  The  Method  of  finding  the  Distances 

hours  17  minutes  41  seconds  for  the  visible  begin- 
ning  of  egress  in  the  morning  at  London. 

56.  At  V  hours  24  minutes  (which  is  the  middle 
of  the  transit,  as  seen  from  the  Earth's  centre)  Lon- 
don will  be  at  L  on  the  Earth's  disc  (Fig.  4.)  as  seen 
from  the  Sun.    The  parallax  La  of  Venus  from  the 
Sun  in  the  direction  of  her  path  is  then  12-J"  ;  by 
which,  working  as  above  directed,  we  find  the  mid- 
dle of  the  transit,  as  seen  from  London,  will  be  at  V 
hours  20  minutes  53  seconds. — This  is  not  affected 
by  Lt  the  parallax  at  right  angles  to  the  path  of  Ve- 
nus.— But  Lt  measures  27"  on  the  scale  AE  (Fig. 
3.) :  therefore  take  '27"  from  the  scale  in  Fig.  1.  and 
set  it  from  t  to  L,  on  the  axis  of  Venus's  path  in 
Fig.  2.  and  laying  a  ruler  to  the  point  />,  and  the 
above- found  point  of  t  gres^  /?,  draw  oLp  for  the  line 
of  the  transit  as  seen  from  London. 

57.  The  eastern  mouth  of  the  river  Ganges  is  89 
degrees  east  from   the  meridian  of  London;    and 
therefore,  when  the  time  at  London  is  28  minutes 
after  II  in  the  morning  (§  40.)  it  is  24  minutes  past 
VIII  in  the  morning  (by  §  47.)  at  the  mouth  of  the 
Ganges  ;  and  when  it  is  twenty  minutes  past  VIII  in 
the  morning  at  London  (§  40.)  it  is  16  minutes  past 
II  in  the  afternoon  at  the  Ganges.     Therefore,  by 
projecting  that  place  upon  the  Earth's  disc,  as  seen 
from  the  Sun,  it  will  be  at  G  (in  Fig.  4.),  at  the  time 
of  Venus's  total  ingress,  as  seen  from  the  Earth's  cen- 
tre, and  at  g  when  her  egress  begins. 

Draw  Ge  and  gr  parallel  to  the  orbit  of  Venus 
VCO,  and  measure  them  on  the  scale  AB  in  Fig.  3. 
the  former  will  be  21"  for  Venus's  eastern  parallax 
in  the  direction  of  her  path,  at  the  above-mentioned 
time  of  her  total  ingress,  and  the  latter  will  be  16*" 
for  her  western  parallax  at  the  time  when  her  egress 
begins. — The  former  parallax  gives  5  minutes  15 
seconds  of  time  (by  the  analogy  in  \  54.)  to  be  ad- 
ded to  VIII  hours  24  minutes,  and  the  latter  paral- 
lax gives  4  minutes  11  seconds  to  be  subtracted 
from  II  hours  16  minutes;  by  which  we  have  VIII 


of  the  Planets  from  the  Sun.  509 

hours  29  minutes  15  seconds,  for  the  time  of  total 
ingress,  as  seen  from  the  banks  of  the  Ganges,  and 
II  hours  1 1  minutes  49  seconds  from  the  beginning 
of  egress,  as  affected  by  these  parallaxes. 

Draw  Of  perpendicular  to  Vrnus's  orbit  VOC, 
and  by  measurement  on  the  scale  AB  (Fig.  3.)  it 
\viil  be  found  to  contain  10" :  take  10"  from  the 
scale  in  Fig.  1.  and  find,  by  trials,  a  point  c,  in  the 
arch  JV,  where,  if  one  foot  of  the  compasses  be  placed, 
the  other  will  just  touch  the  central  transit-line  kl. 
Take  the  nearest  distance  from  this  point  c  to  CL, 
the  axis  of  Venus's  orbit,  and  applying  it  from  t  to- 
ward k,  you  will  find  it  fall  a  minute  short  of  k ; 
which  shows,  that  Venus's  parallax  in  this  direction 
shortens  the  beginning  of  the  line  of  her  visible  tran- 
sit at  the  Ganges  by  one  minute  of  time.  Therefore, 
as  this  makes  the  visible  ingress  a  minute  later,  add 
one  minute  to  the  above  VIII  hours  29  minutes  15 
seconds,  and  it  will  give  VIII  hours  30  minutes  15 
seconds  for  the  lime  of  total  ingress  in  the  morning, 
as  seen  from  -he  eastern  mouth  of  the  Ganges.  At 
the  beginning  of  egress,  the  parallax  gp  in  the  same 
direction  is  21?"  (by  measurement  on  the  scale  AB), 
which  will  protract  the  beginning  of  egress  by  about 
30  seconds  of  time,  and  must  therefore  be  added  to 
the  above  II  hours  1 1  minutes  49  seconds,  which 
will  make  the  visible  beginning  of  egress  to  be  at  II 
hours  12  minutes  19  seconds  in  the  afternoon. 

58.  Bencoolen  is  102  degrees  east  from  the  meri- 
dian of  London  ;  and  therefore,  when  the  time  is  28 
minutes  past  1  f  in  the  morning  at  London,  it  is  16 
minutes  past  IX  in  the  morning  at  Bencoolen;  and 
when  it  is  20  minutes  past  VIII  in  the  morning  at 
London,  it  is  8  minutes  past  III  in  the  afternoon  at 
Bencoolen.  Therefore,  in  Fig.  4.  Bencoolen  will  be 
at  B  at  the  time  of  Venus's  total  ingress,  as  seen 
from  the  Earth's  centre ;  and  at  b  when  her  egress 
begins. 


510  7%?  Method  of  finding  the  Distances 

Draw  El  and  bk  parallel  to  Venus's  orbit 
and  measure  them  on  the  scale :  the  former  will  be 
found  to  be  22"  for  Venus's  eastern  parallax  in  the 
direction  of  her  path  at  the  time  of  her  total  ingress ; 
and  the  latter  to  be  19-J"  for  her  western  parallax  in 
the  same  direction  when  her  egress  begins,  as  seen 
from  the  Earth's  centre.  The  first  of  these  parallaxes 
gives  5  minutes  30  seconds  (by  the  analogy  in  §  54.) 
to  be  added  to  IX  hours  16  minutes,  and  the  latter 
parallax  gives  4  minutes  52  seconds  to  be  subtracted 
from  III  hours  8  minutes ;  whence  we  have  IX 
hours  21  minutes  30  seconds  for  the  time  of  total 
ingress  at  Bencoolen :  and  III  hours  3  minutes  and 
8  seconds  for  the  time  when  the  egress  begins  there, 
as  affected  by  these  two  parallaxes. 

59.  Draw  bv  and  bm  perpendicular  to  Venus's 
orbit  VCO,  and  measure  them  on  the  scale  AB :  the 
former  will  be  5"  for  Venus's  northern  parallax  in  a 
direction  perpendicular  to  her  path,  as  seen  from 
Bencoolen^  at  the  time  of  her  total  ingress ;  and  the 
latter  will  be  15£"  for  her  northern  parallax  in  that 
direction  when  her  egress  begins.  Take  these  pa- 
rallaxes from  the  scale,  Fig.  1.  in  your  compasses, 
and  find,  by  trials,  two  points  in  the  arcs  JVand  T 
(Fig.  2.)  where  if  one  foot  of  the  compasses  be 
placed,  the  other  will  touch  the  central  transit- line 
kl:  draw  a  line  from  a  to  6,  for  the  line  of  Venus's 
transit  as  seen  from  Bencoolen  ;  the  centre  of  Venus 
being  at  a,  as  seen  from  Bencoolen,  at  the  moment 
of  her  total  ingress ;  and  at  b  at  the  moment  when 
her  egress  begins. 

But  as  seen  from  the  Earth's  centre,  the  centre 
of  Venus  is  at  k  in  the  former  case,  and  at  /  in  the 
latter :  so  that  we  find  the  line  of  the  transit  is 
longer  as  seen  from  Bencoolen  than  as  seen  from  the 
Earth's  centre,  which  is  the  effect  of  Venus's  north- 
ern parallax. — Take  Ba  in  your  compasses,  and 
setting  that  extent  backward  from  t  toward  .g,  on 
the  central  transit-line,  you  will  find  it  will  reach 
two  minutes  beyond  k :  and  taking  the  extent  Bb 


of  the  Planets  from  the  Sun.  511 

in  your  compasses,  and  setting  it  forward  from  t  to- 
ward iv,  on  the  central  transit- line,  it  will  be  found 
to  reach  3  minutes  beyond  /.  Consequently,  if  we 
subtract  2  minutes  from  IX  hours  21  minutes  30 
seconds  (above  found),  we  have  IX  hours  19  mi- 
nutes 30  seconds  in  the  morning,  for  the  time  of 
total  ingress,  as  seen  from  Bencoolen :  and  if  we  add 
3  minutes  to  the  above-found  III  hours  3  minutes 
$  seconds,  we  shall  have  III  hours  6  minutes  8  se- 
conds afternoon,  for  the  time  when  the  egress  be- 
gins, as  seen  from  Bencoolen. 

60.  The  whole  duration  of  the  transit,  from  the 
total  ingress  to  the  beginning  of  egress,  as  seen  from 
the  Earth's  centre,  is  5  hours  52  minutes  (by  §  40.); 
but  the  whole  duration  from  the  total  ingress  to  the 
beginning  of  egress,  as  seen  from  Bencoolen,  is  only 
5  hours  46  minutes  38  seconds :  which  is  5  minutes 
22  seconds  less  than  as  seen  from  the  Earth's  cen- 
tre :  and  this  5  minutes  22  seconds  is  the  whole 
effect  of  the  parallaxes  (both  in  longitude  and  lati- 
tude) on  the  duration  of  the  transit  at  Bencoolen. 

But  the  duration,  as  seen  at  the  mouth  of  the 
Ganges,  from  ingress  to  egress,  is  still  less ;  for  it 
is  only  5  hours  42  minutes  4  seconds ;  which  is  9 
minutes  56  seconds  less  than  as  seen  from  the  Earth's 
centre,  and  4  minutes  34  seconds  less  than  as  seen 
at  Bencoolen. 

61.  The  island  of  St.  Helena  (to  which  only  a 
small  part  of  the  transit  is  visible  at  the  end)  will 
be  at  H  (as  in  Fig.  4.-)  when  the  egress  begins  as 
seen  from  the  Earth's  centre.     And  since  the  mid- 
dle of  that  island  is  6°  west  from  the  meridian  of 
London,  and  the  said  egress  begins  when  the  time 
at  London  is  20  minutes  past  VIII  in  the  morning, 
it  will  then  be  only  56  minutes  past  VII  in  the 
morning  at  St.  Helena. 

Draw  Hn  parallel  to  Venus's  orbit  VCO,  and 
Ho  perpendicular  to  it ;  and  by  measuring  them  on 
the  scale  AB  (Fig.  3.)  the  former  will  be  found  to 
amount  to  29"  for  Venus's  eastern  parallax  in  the 

3T 


5,12  The  Method  of  finding  the  Distances 

direction  of  her  path,  as  seen  from  St.  Helena,  when 
her  egress  begins,  as  seen  from  the  Earth's  centre  ; 
and  the  latter  to  be  6"  for  her  northern  parallax  in 
a  direction  at  right  angles  to  her  path. 

By  the  analogy  in  $  54,  the  parallax  in  the  direc- 
tion of  the  path  of  Venus  gives  10  minutes  2  se- 
conds of  time;  which  being  added  (on  account  of 
its  being  eastward)  to  VII  hours  56  minutes,  gives 
VIII  hours  6  minutes  2  seconds  for  the  beginning 
of  egress  at  St.  Helena,  as  affected  by  this  parallax. 
• — But  6"  of  parallax  in  a  perpendicular  direction  to 
her  path  (applied  as  in  the  case  of  Bcncoolen)  length- 
ens  out  the  end  of  the  transit-line  by  one  minute  ; 
\vhich  being  added  to  VIII  hours  6  minutes  2  se- 
conds, gives  VIII  hours  7  minutes  2  seconds  for  the 
beginning  of  egress,  as  seen  from  St.  Helena. 

62.  We  shall  now  collect  the  above-mentioned 
times  into  a  small  table,  that  they  may  be  seen  at 
once,  as  follows :  M  signifies  morning,  A  afternoon. 


Total  ingress. 

H.  M.S. 

f  The  Earth's  centre  II  28  OM 
}  London  -  -  -  Invisible  M 
^  The  Ganges  mouth  VIII 30  15 M 
\  Bencoolen  -  -  IX  19  30 M 
{.St.  Helena  -  -  Invisible  M 


Beg.  of  egress. 

H.  M.  S. 

VIII  20    OM 

VIII  17  41M 

II  12  19  A 

III  68^ 

V11I  7     12M 


Duration. 
H.  M.  S. 
5  52  0* 


5    42    4 
5     46  38 


63.  The  times  at  the  three  last-mentioned  places 
are  reduced  to  the  meridian  of  London,  by  sub- 
tracting 5  hours  56  minutes  from  the  times  of  in- 
gress and  egress  at  the  Ganges;  6  hours  48  mi- 
nutes from  the  times  at  Bencoolen ;  and  adding  24 

*  This  duration  as  seen  from  the  Earth's  centre,  is  on  supposition 
that  the  semidiameter  of  Venus  would  be  found  equal  to  37 1 ",  on  the 
bun's  disc  as  stated  by  Dr.  If  alley  (see  Art.  V.  §  31.),  to  which  all 
the  other  durations  are  accommodated. — But,  from  later  observa- 
tions, it  is  highly  probable,  that  the  semidiameter  of  Venus  will  be 
found  not  to  exceed  30"  on  the  Sun ;  and  if  so,  the  duration  between 
the  two  internal  contacts,  as  seen  from  the  Earth's  centre,  will  be  5 
hours  58  minutes ;  and  the  duration  as  seen  from  the  above-men- 
tioned places,  will  be  lengthened  very  nearly  in  the  same  proportion. 


of  the  Planets  from  the  Sun.  513 

minutes  to  the  time  of  beginning  of  egress  at  St. 
Helena:  and  being  thus  reduced,  they  are  as  fol- 
lows : 


Total  Ingress. 

H.M.S. 

Times  at  C  Ganges  mouth     11  34  15 M 
London  <  Hencoolen     -    -  II  31  30  A/ 
for         &•  Helena  -    -  Invisible  M 


Beg.  of  egress. 

II.  M.S? 

V11I  16  19 M-)  Dura- 
V11I  18  8MC  lions  as 
V1I1  31  2A/S  above. 


64  All  this  is  on  supposition,  that  we  have  the 
true  longitudes  of  the  three  last- mentioned  places, 
that  the  Sun's  horizontal  parallax  is  12£;/  that  the 
true  latitude  of  Venus  is  given,  and  that  her  semi- 
diameter  will  subtend  an  angle  of  37-1"  on  the  Sun's 
disc.  P 

As  for  the  longitudes,  we  must  suppose  them  true, 
until  the  observers  ascertain  them,  which  is  a  very 
important  part  of  their  business;  and  without  which 
they  can  by  no  means  find  the  interval  of  absolute 
lime  that  -elapses  between  either  the  ingress  or  egress, 
as  seen  from  any  two  given  places :  and  there  is 
much  greater  dependence  to  be  had  on  this  elapse, 
than  upon  the  whole  contraction  of  duration  at  any 
given  place,  as  it  will  undoubtedly  afford  a  surer 
basis  for  determining  the  Sun's  parallax. 

65.  I  have  good  reason  to  believe  that  the  latitude 
of  Venus,  as  given  in  §  31,  will  be  found  by  obser- 
vation to  be  very  near  the  truth ;  but  that  the  time 
of  conjunction  there  mentioned  will  be  found  later 
than  the  true  time  by  almost  5  minutes ;  that  Venus's 
semidiameter  will  subtend  an  angle  of  no  more  than 
30"  on  the  Sun's  disc ;  and  that  the  middle  of  her 
transit  as  seen  from  the  Earth's  centre,  will  be  at  24 
minutes  after  V  in  the  morning,  as  reckoned  by  the 
equal  time  at  London. 

66.  Subtract  V11I  hours  17  minutes  41  seconds, 
the  time  when  the  egress  begins  at  London,  from 
VIII  hours  31  minutes  2  seconds,  the  time  reckoned 
ut  London  when  the  egress  begins  at  St.  Helena ,  and 


514  The  Method  of  finding  the  Distances 

there  will  remain  13  minutes  21  seconds  (or  801  se- 
conds) for  their  difference  or  elapse,  in  absolute  time, 
between  the  beginning  of  egress,  as  seen  from  these 
two  places. 

Divide  801  seconds  by  the  Sun's  parallax  12i", 
and  the  quotient  will  be  64  seconds  and  a  small  frac- 
tion. So  that  for  each  second  of  a  degree  in  the 
Sun's  horizontal  parallax  (supposing  it  to  be  1%%') 
there  will  be  a  difference  or  elapse  of  64  seconds  of 
absolute  time  between  the  beginning  of  egress  as 
seen  from  London,  and  as  seen  from  St.  Helena; 
and  consequently  32  seconds  of  time  for  every  half 
second  of  the  Sun's  parallax;  16  seconds  of  time  for 
every  fourth  part  of  a  second  of  the  Sun's  parallax  ; 
8  seconds  of  time  for  the<  eighth  part  of  a  second  of 
the  Sun's  parallax;  and  full  4  seconds  for  a  sixteenth 
part  of  the  Sun's  parallax.  For  in  so  small  an  angle 
as  that  of  the  Sun's  parallax,  the  arc  is  not  sensibly 
different  from  either  its  sine  or  its  tangent:  and 
therefore  the  quantity  of  this  parallax  is  in  direct 
proportion  to  the  absolute  difference  in  the  time  of 
egress  arising  from  it  at  different  parts  of  the  Earth. 

67.  Therefore,  when  this  difference  is  ascertained 
by  good  observations,  made  at  different  places,  and 
compared  together,  the  true  quantity  of  the  Sun's 
parallax    will    be   very    nearly    determined.      For, 
since  it  may  be  presumed  that  the    beginning  of 
egress  can  be  observed  within  2  seconds  of  its  real 
time,  the  Sun's  parallax  may  then  be  found  within 
the  32d  part  of  a  second  of  its  true  quantity ;  and 
consequently,  his  distance  may  be  found  within  a 
400th  part  of  the  whole,  provided  his  parallax  be 
not  less  than  123" ;  for  32  times  12-J  is  400. 

68.  But  since  Dn.  HAL  LEY  has  assured  us,  that 
he  had  observed  the  two  internal  contacts  of  the 
planet  Mercury  with  the  Sun's  edge  so  exactly  as 
not  to  err  one  second  in  the  time,  we  may  well  im- 
agine that  the  internal  contacts  of  Venus  with  the 
Sun  may  be  observed  with  as  great  accuracy.     So 


of  the  Planets  from  the  Sun.  515 

that  we  may  hope  to  have  the  absolute  interval  be- 
tween the  moments  of  her  beginning  of  egress,  as 
seen  from  London,  and  from  St.  Helena,  true  to  a 
second  of  time ;  and  if  so,  the  Sun's  parallax  may  be 
determined  to  the  64th  part  of  a  second,  provided 
it  be  not  less  than  1 2i"  :  and  consequently  his  dis- 
tance may  be  found,  within  its  800th  part;  for  64 
times  12?  is  800 :  which  is  still  nearer  the  truth 
than  Dr.  H ALLEY  expected  it  might  be  found  by 
observing  the  whole  duration  of  the  transit  in  the 
East-Indies  and  at  Port-Nelson.  So  that  our  pre- 
sent astronomers  have  judiciously  resolved  to  improve 
the  Doctor's  method,  by  taking  only  the  interval  be- 
tween the  absolute  times  of  its  ending  at  different 
places.  If  the  Sun's  parallax  be  greater  or  less  than 
12^",  the  elapse  or  difference  of  absolute  time  between 
the  beginning  of  egress  at  London  and  at  St.  Helena^ 
will  be  found  by  observation  to  be  greater  or  less 
than  801  seconds  accordingly. 

69.  There  will  also  be  a  great  difference  between 
the  absolute  times  of  egress  at  St.  Helena  and  the 
northern  parts  of  Russia,  which  would  make  these 
places  very  proper  for  observation.     The  difference 
between  them  at  Tobolsk  in  Siberia,  and  at  St.  Hele- 
7ia,  will  be  11  minutes,  according  to  DE  L'!SLE'S 
map  :  at  Archangel  it  will  be  but  about  40  seconds 
less  than  at  Tobolsk  ;  and  only  a  minute  and  a  quar- 
ter less  at  Petersbnrgh,  even  if  the  Sun's  parallax 
be  no  more  than  1GJ".     At  Wardhus  the  same  ad- 
vantage would  nearly  be  gained  as  at  Tobolsk  ;  but  if 
the  observers  could  go  still  farther  to  the  east,  as  to 
Yakoutsk  in  Siberia,  the  advantage  would  be  still 
greater:    for,    as  M.  DE  L'!SLE  very  justly  ob- 
serves, in  a  memoir  presented  to  the  French  king 
with  his  map  of  the  transit,  the  difference  of  time 
between  Venus's  egress  from  the  Sun  at  Yakoutsk 
and  at  the  Cape  of  Good  Hope  will  be  13|  minutes. 

70.  This  method  requires  that  the  longitude  of 
each  place  of  observation   be    ascertained  to  the 


516  The  Method  of  finding  the  Distances 

greatest  degree  of  nicety,  and  that  each  observer's 
clock  be  exactly  regulated  to  the  equal  time  at  his 
place  :  for  without  these  particulars  it  would  be  im- 
possible for  the  observers  to  reduce  the  times  to  those 
which  are  reckoned  under  any  given  meridian  ;  and 
without  reducing  the  observed  times  of  egress  at  dif- 
ferent places  to  the  time  at  some  given  place,  the  ab- 
solute time  that  elapses  between  the  egress  at  one 
place  and  at  another  could  not  be  found.  But  the 
longitudes  may  be  found  by  observing  the  eclipses 
of  Jupiter's  satellites ;  and  a  true  meridian,  for  regu- 
lating the  clock,  to  the  time  at  any  place,  may  be  had 
by  observing  when  any  given  star  within  20  or  30 
degrees  of  the  pole,  is  stationary  with  regard  to  its 
azimuth  on  the  east  and  west  sides  of  the  pole  ;  the 
pole  itself  being  the  middle  point  between  these  two 
stationary  positions  of  the  star.  And  it  is  not  mate- 
rial for  the  observers  to  know  exactly  either  the  true 
angular  measure  of  the  Sun's  diameter,  or  of  Venus's, 
in  this  case ;  for  whatever  their  diameters  be,  it  will 
make  no  sensible  difference  in  the  observed  interval 
between  the  same  contact,  as  seen  from  different 
places. 

71.  In  the  geometrical  construction  of  transits, 
the  scale  AE  (Fig,  3.  of  Plate  XVI)  may  be  di- 
vided into  any  given  number  of  equal  parts,  an- 
swering to  any  assumed  quantity  of  Venus's  hori- 
zontal parallax  from  the  JSun  (which  is  always  the 
difference  between  the  horizontal  parallax  of  Venus 
and  that  of  the  Sun),  provided  the  whole  length  of 
the  scale  be  equal  to  the  semidiameter  of  the  Earth's 
disc  in  Fig.  4. — Thus  if  we  suppose  Venus's  hori- 
zontal parallax  from  the  Sun  to  be  only  26"  (in- 
stead of  31")  in  which  case  the  Sun's  horizontal 
parallax  must  be  10".3493,  as  in  §  20,  the  rest  of 
the  projection  will  answer  to  that  scale:  as  CD, 
which  contains  only  26  equal  parts,  is  the  same 
length  as  AB,  which  contains  31.  And  by  work- 
ing in  all  other  respects  as  taught  from  i  45  to 


of  the  Planets  from  the  Sun.  517 

§  62,  you  will  find  the  times  of  total  ingress  and  be- 
ginning of  egress ;  and  consequently  the  duration  of 
the  transit  ur  any  given  place,  which  musi  result  from 
such  a  parallax. 

72.  In  projections  of  this  kind,  it  may  be  easily 
conceived,  that  a  right  line  passing  continually 
through  the  centre  of  Venus,  and  a  given  point  of 
the  Earth,  and  produced  to  the  Sun's  disc,  will 
mark  the  path  of  Venus  on  the  Sun,  as  seen  from 
the  given  point  of  the  Earth :  and  in  this  there  are 
three  cases.  1»  When  the  given  point  is  the 
Earth's  centre,  at  \vhich  there  is  no  parallax,  either 
in  longitude  or  latitude.  2.  When  the  given  point 
is  one  of  the  poles,  where  there  is  no  parallax  of 
longitude  ;  but  a  parallax  of  latitude,  whose  quantity 
is  easily  determined,  by  letting  fall  a  perpendicular 
from  the  pole  upon  the  plane  of  the  ecliptic,  and  set- 
ting off  the  parallax  of  latitude  on  this  perpendicu- 
lar :  and  here  the  polar  transit-lines  will  be  parallel 
to  the  central,  as  the  poles  have  no  motion  arising 
from  the  Earth's  diurnal  rotation.  3.  The  last  case 
is,  when  the  given  point  of  the  Earth  is  any  point  of 
its  surface,  whose  latitude  is  less  than  90  degrees : 
then  there  is  a  parallax  in  latitude  proportional  to  the 
perpendicular  let  fall  upon  the  abovesaid  plane,  from 
the  given  point ;  and  a  parallax  in  longitude  propor- 
tional to  the  perpendicular  let  fall  upon  the  axis  of 
that  plane,  from  the  said  given  point.  And  the  effect 
of  this  last  will  be  to  alter  the  transit-line,  both  in  po- 
sition and  length  ;  and  will  prevent  its  being  parallel 
to  the  central  transit-line,  unless  when  its  axis  and 
the  axis  of  the  Earth  coincide,  as  seen  from  the 
Sun;  which  is  a  thing  that  may  not  happen  in  many 
ages. 


518  The  Method  of  finding  the  Distances 

ARTICLE  VI. 

Concerning  the  map  of  the  transit.     Plate  XVIL 

73.  The  title  of  this  map,  and  the  lines  drawn 
upon  it,  together  with  the  words  annexed  to  these 
lines,  and  the  numbers  (hours  and  minutes)  on  the 
clotted  lines,  explain  the  whole  of  it  so  well,  that  no 
farther  description  seems  requisite. 

74.  So  far  as  I  can  examine  the  map  by  a  good 
globe,  the  black  curve-lines  are  in  general  pretty 
well  laid  down,  for  shewing  at  what  places  the  tran- 
sit will  begin,  or  end,  at  sun-rising  or  sun-setting,  to 
all  those  places  through  which  they  are  drawn,  ac- 
cording to  the  times  mentioned  in  the  map.    Only  I 
question  much  whether  the  transit  will  begin  at  sun- 
rise to  any  place  in  Africa,  that  is  west  of  the  Red- 
Sea  ;  and  am  pretty  certain  that  the  Sun  will  not  be 
risen  to  the  northernmost  part  of  Madagascar  when 
the  transit  begins,  as  M.  DEL'IsLE  reckons  the 
first  contact  of  Venus  with  the  Sun  to  be  the  begin- 
ning  of  the  transit.     So  that  the  line  which  shews 
the  entrance  of  Venus  on  the  Sun's  disc  at  sun-ris- 
ing, seems  to  be  a  little  too  far  west  in  the  map,  at 
all  places  which  are  south  of  Asia  Minor :  but  in 
JEurope,  I  think  it  is  very  well. 

75.  In   delineating  this   map,    I  had  M.  DE 
L'IsLE's  map  of  the  transit  before  me.     And  the 
only  difference  between  his  map   and   this,  is,  1. 
That  in  his  map,  the  times  are  computed  to  the 
meridian  of  Paris;  in  this  they  are  reduced  to  the 
meridian  of  London.     2.  I  have  changed  his'ineri- 
dional  projection   into  that  of  the  equatorial;    by 
which,    I  apprehend    that    the   black  curve. lines, 
shewing  at  what  places  the  transit  begins,  or  ends, 
with  the  rising  or  setting  Sun,  appear  more  natural 
to  the  eye,  and  are  more  fully  seen  at  once,  than  in 
the  map  from  which  I  copied ;  for  in  that  map  the 
lines  are  interrupted  and  broken  in  the  meridian 


of  the  Planets  from  the  Sun.  519 

that  divides  the  hemispheres  ;  and  the  places  where 
thu-y  should  join  cannot  be  perceived  so  readily  by 
those  who  are  not  well  skilled  in  the  nature  of  ste- 
rtographical  projections. — The  like  may  be  said  of 
many  of  the  dotted  curve-lines,  on  which  are  ex- 
pressed the  hours  and  minutes  of  the  beginning  or 
ending  of  the  transit,  which  are  the  absolute  times 
at  these  places  through  which  the  lines  are  drawn, 
computed  to  the  meridian  of  London. 


ARTICLE  VII. 

Containing  an  account  of  Mr.  Ho  R  R  ox's  observation 
of  the  transit  of  Venus  over  the  Sun,  in  the  year 
1639;  as  it  is  published  in  the  Annual  Register 
for  the  year  1761. 

76.  When  Kepler  first  constructed  his  (the  Ru- 
dolphine)  tables  upon  the  observations  of  Tycho> 
he  soon  became  sensible  that  the  planets  Me  rcury 
and  Venus  would  sometimes  pass  over  the  Sun's 
disc  ;  and  he  predicted  two  transits  of  Venus,  one 
for  the  year  1631,  and  the  other  for  1761,  in  a 
tract  published  at  Leipsick  in  1629,  iniitled,  Ad- 
monitio  ad  Astronomos,  &c.  Kepler  died  some  days 
before  the  transit  in  1631,  which  he  had  predicted 
was  to  happen.  Gassendi  looked  for  it  at  Paris,  but 
in  vain  (ste  Mercurius  in  Sole  vtsus,  &  Venus 
invisa].  In  fact,  the  imperfect  state  of  the  Rudol- 
phine  tables  was  the  cause  that  the  transit  was  expect, 
ed  in  1631,  when  none  could  be  observed;  and  those 
very  tables  did  not  give  reason  to  expect  one  in 
1639,  when  one  was  really  observed. 

When  our  illustrious  countryman  Mr.  HORROX 
first  applied  himself  to  astronomy,  he  computed 
ephemerides  for  several  years,  from  jLansbergius's 
tables.  After  continuing  his  labours  for  some  time, 
he  was  enabled  to  discover  the  imperfection  of  these 
tables;  upon  which  he  laid  aside  his  work,  intending 
3  V 


520  The  Method  of  finding  the  Distances 

to  determine  the  positions  of  the  stars  from  his  own 
observations.  But  that  the  former  part  of  his  time 
spent  in  calculating  from  Lansbergius  might  not  be 
thrown  away,  he  made  use  of  his  ephemerides  to 
point  out  to  him  the  situations  of  the  planets.  Hence 
he  foresaw  when  their  conjunctions,  their  appulses 
to  the  fixed  stars,  and  the  most  remarkable  pheno- 
mena in  the  heavens  would  happen  ;  and  prepared 
himself  with  the  greatest  care  to  observe  them. 

Hence  he  was  encouraged  to  wait  for  the  important 
observation  of  the  transit  of  Venus  in  the  year  1639  ; 
and  no  longer  thought  the  former  part  of  his  time 
mispent,  since  his  attention  to  Lansbergius^  tables 
had  enabled  him  to  discover  that  the  transit  would 
certainly  happen  on  the  24th  of  November.  However, 
as  these  tables  had  so  often  deceived  him,  he  was 
unwilling  to  rely  on  them  entirely,  but  consulted 
other  tables,  and  particularly  those  of  Kepler :  ac- 
cordingly in  a  letter  to  his  friend  William  Crabtree, 
of  Manchester,  dated  Hool,  October  26,  1639,  he 
communicated  his  discovery  to  him,  and  earnestly 
desired  him  to  make  whatever  observations  he  possi- 
hly  could  w  ith  his  telescope,  particularly  to  measure 
the  diameter  of  the  planet  Venus  ;  which,  according 
to  Kepler ',  would  amount  to  7  minutes  of  a  degree, 
and  according  to  Lansbergius  to  11  minutes  ;  but 
which,  according  to  his.  own  proportion,  he  expected 
would  hardly  exceed  one  minute.  He  adds,  that 
according  to  Kepler,  the  conjunction  will  be  No- 
vember 24,  1639,  at  8  hours  1  minute  A.  M.  at 
Manchester,  and  that  the  planet's  latitude  would  be 
14'  10"  south  ;  but  according  to  his  own  corrections 
he  expected  it  to  happen  at  3  hours  57  min.  P.  M. 
at  Manchester,  with  10'  south  latitude.  But  be- 
cause a  small  alteration  in  Kepler^s  numbers  would 
greatly  alter  the  time  of  conjunction,  and  the  quan- 
tity of  the  planet's  latitude,  he  advises  to  watch  the 
whole  day,  and  even  on  the  preceding  afternoon,  and 
the  morning  of  the  25th,  though  he  was  entirely  of 
opinion  that  the  transit  would  happen  on  the  24th. 


of  the  Planets  from  the  Sun. 

After  having  fully  weighed  and  examined  the  se- 
veral methods  of  observing  this  uncommon  pheno- 
menon, he  determined  to  transmit  the  Sun's  image 
through  a  telescope  into  a  dark  chamber,  rather  than 
through  a  naked  aperture,  a  method  greatly  com- 
mended by  Kepler;  for  the  Sun's  image  is  not  given 
sufficiently  large  and  distinct  by  the  latter,  unless  at 
a  very  great  distance  from  the  aperture,  which  the 
narrowness  of  his  situation  would  not  allow  of;  nor 
would  Venus's  diameter  be  well  defined,  unless  the 
aperture  were  very  small ;  whereas  his  telescope, 
which  rendered  the  solar  spots  distinctly  visible, 
would  shew  him  Venus's  diameter  well  defined, 
and  enable  him  to  divide  the  Sun's  limb  more  accu- 
rately. 

He  described  a  circle  on  paper  which  nearly  equal- 
led six  inches,  the  narrowness  of  the  place  not  al- 
lowing a  larger  size  ;  but  even  this  size  admitted  di- 
visions sufficiently  accurate.  He  divided  the  cir- 
cumference into  360  degrees,  and  the  diameter  into 
30  equal  parts,  each  of  which  was  subdivided  into 
4,  and  the  whole  therefore  into  120.  The  subdivi- 
sion might  have  still  been  carried  farther,  but  he 
trusted  rather  to  the  accuracy  and  niceness  of  his 
eye. 

When  the  time  of  observation  drew  near,  he  ad- 
justed the  apparatus,  and  caused  the  Sun's  distinct 
image  exactly  to  fill  the  circle  on  the  paper :  and 
though  he  could  not  expect  the  planet  to  enter  upon 
the  Sun's  disc  before  three  o'clock  in  the  afternoon 
of  the  24th,  from  his  own  corrected  numbers,  upon 
which  he  chiefly  relied ;  yet,  because  the  calcula- 
tions in  general  from  other  tables  gave  the  time  of 
conjunction  much  sooner,  and  some  even  on  the 
23d,  he  observed  the  Sun  from  the  time  of  its  rising 
till  nine  o'clock ;  and  again,  a  little  before  ten,  at 
noon,  and  at  one  in  the  afternoon;  being  called  in 
the  intervals  to  business  of  the  highest  moment, 
which  he  could  not  neglect.  But  in  all  these  times 


522  The  Method  of  finding  the  Distances 

he  saw  nothing  on  the  Sun's  face,  except  one  small 
spot,  which  he  had  seen  on  the  preceding  day  ;  and 
\vhich  also  he  afterward  saw  on  some  of  the  follow- 
ing days. 

But  at  3  hours  15  minutes  in  the  afternoon, 
which  was  the  first  opportunity  he  had  of  repeating 
his  observations,  the  clouds  were  entirely  dispersed, 
and  invited  him  to  seize  this  favourable  occasion, 
which  seemed  to  be  providentially  thrown  in  his  way; 
for  he  then  beheld  the  most  agreeable  sight,  a  spot, 
which  had  been  the  object  of  his  most  sanguine 
wishes,  of  an  unusual  size,  and  of  a  perfectly  circular 
shape,  just  whol!y  entered  upon  the  Sun's  disc  on 
the  left  side :  so  that  the  limbs  of  the  Sun  and  Venus 
perfectly  coincided  in  every  point  of  contact.  He 
was  immediately  sensible  that  this  spot  was  the  planet 
Venus,  and  applied  himself  with  the  utmost  care  to 
prosecute  his  observations. 

And,  First,  with  regard  to  the  inclination,  he 
found,  by  means  of  a  diameter  of  the  circle  set  per- 
pendicular to  the  horizon,  the  plane  of  the  circle 
being  somewhat  reclined  on  account  of  the  Sun's 
altitude,  that  Venus  had  wholly  entered  upon  the 
Sun's  disc,  at  3  hours  15  minutes,  at  about  62°  30' 
(certainly  between  60°  and  65°)  from  the  vertex 
tov  ard  the  right  hand.  (These  were  the  appear- 
ances within  the  dark  chamber,  where  the  Sun's 
image  and  motion  of  the  planet  on  it  were  both  in- 
verted and  reversed.)  And  this  inclination  continu- 
ed constant,  at  least  to  all  sense,  till  he  had  finished 
the  whole  of  his  observation. 

Secondly,  The  distances  observed  afterward  be- 
tween the  centres  of  the  Sun  and  Venus  were  as  fol- 
lows :  At  3  hours  15  minutes  by  the  clock,  the  dis- 
tance was  14'  24";  at  3  hours  35  minutes,  the  dis- 
tance was  13'  30"  ;  at  3  hours  45  minutes,  the  dis- 
tance was  13'  0".  The  apparent  time  of  sun- setting 
was  at  3  hours  50  minutes — the  true  time  3  hours 


of  the  Planets  from  the  Sun.  523 

15  minutes, — refraction  keeping  the  Sun  above  the 
hoiizon  for  the  space  of  5  minutes. 

Thirdly,  He  found  Venus's  diameter,  by  repeated 
observations,  to  exceed  a  thirtieth  part  of  the  Sun's 
diameter,  by  a  sixth,  or  at  most  a  fifth  subdivision. 
— The  diameter  therefore  of  the  Sun  to  that  of  Ve- 
nus may  be  expressed  as  30  to  1.12.  It  certainly 
did  not  amount  to  1.30,  nor  yet  to  1.20.  And  this 
was  found  by  observing  Venus  as  weii  when  near  the 
Sun's  limb,  as  when  farther  removed  from  it. 

The  place  where  this  observation  was  made,  was 
an  obscure  village  called  Hool,  about  15  miles  north- 
ward of  Liverpool  The  latitude  of  Liverpool  had 
been  often  determined  by  Horrox  to  be  53°  20'; 
and  therefore,  that  of  Hool  will  be  53°  35'.  The 
longitude  of  both  seemed  to  him  to  be  about  22°  30' 
from  the  Fortunate  Islands:  that  is,  14°  15'  to  the 
west  of  Uraniburg. 

These  were  all  the  observations  which  the  short- 
ness of  the  time  allowed  him  to  make  upon  this  most 
remarkable  and  uncommon  sight ;  all  that  could  be 
done,  however,  in  so  small  a  space  of  time,  he  very 
happily  executed;  and  scarce  any  thing  farther  re- 
mained for  him  to  desire.  In  regard  to  the  inclina- 
tion alone,  he  could  not  obtain  tht  utmost  exactness; 
for  it  was  extremely  difficult,  from  the  Sun's  rapid 
motion,  to  observe  it  to  any  certainty  within  the  de- 
gree. And  he  ingenuously  confesses  that  he  neither 
did,  nor  could  possibly  perform  it.  The  rest  are 
very  much  to  be  depended  upon ;  and  as  exact  as  he 
could  wish. 

Mr.  Crabtree,  at  Manchester,  whom  Mr.  Hot- 
rox  had  desired  to  observe  this  transit,  and  who  in 
mathematical  knowledge  was  inferior  to  few,  very 
readily  complied  with  his  friend's  request;  but  the 
sky  was  very  unfavourable  to  him,  and  he  had  only 
one  sight  of  Venus  on  the  Sun's  disc,  which  was 
about  3  hours  35  minutes  by  the  clock ;  the  Sun 
then,  for  the  first  time,  breaking  out  from  the  clouds: 


524  The  Method  of  finding  the  Distances 


at  which  time  he  sketched  out  Venus's  situation  up- 
on paper,  which  Horrox  found  to  coincide  with  his 
own  observations. 

Mr.  Horrox,  in  his  treatise  on  this  subject  pub- 
lished by  Hevelius,  and  from  which  almost  the 
whole  of  this  account  has  been  collected,  hopes  for 
pardon  from  the  astronomical  world,  for  not  making 
his  intelligence  more  public  ;  but  his  discovery  was 
made  too  late.  He  is  desirous,  however,  in  the  spirit 
of  a  true  philosopher,  that  other  astronomers  were 
happy  enough  to  observe  it,  who  might  either  con- 
firm or  correct  his  observations.  But  such  confi- 
dence was  reposed  in  the  tables  at  that  time,  that  it 
does  not  appear  that  this  transit  of  Venus  was  observ- 
ed by  any  besides  our  two  ingenious  countrymen, 
who  prosecuted  their  astronomical  studies  with  such 
eagerness  and  precision,  that  they  must  very  soon 
have  brought  their  favourite  science  to  a  degree  of 
perfection  unknown  at  those  times.  But  unfortunate- 
ly Mr.  Horrox  died  on  the  3d  of  January  1640-1, 
about  the  age  of  25,  just  after  he  had  put  the  last 
hand  to  his  treatise,  intitled  Venus  In  Sole  visa,  in 
which  he  shews  himself  to  have  had  a  more  accurate 
knowledge  of  the  dimensions  of  the  solar  system 
than  his  learned  commentator  Hevelius. — So  far  the 
Annual  Register. 

In  the  year  1691*,  Dr.  HALLE  Y  gave  in  a  paper 
upon  the  transit  of  Venus  (See  Lowthorpe^^  Abridg- 
ment of  Philosophical  Transactions,  page  434.),  in 
which  he  observes,'  from  the  tables  then  in  use,  that 
Venus  returns  to  a  conjunction  with  the  Sun  in  her 
ascending  node  in  a  period  of  18  years,  wanting  2 
days  10  hours  521  minutes;  but  that  in  the  second 
conjunction  she  will  have  got  24'  41"  farther  to  the 
south  than  in  the  preceding.  That  after  a  period  of 
235  years  2  hours  10  minutes  9  seconds,  she  returns 
to  a  conjunction  more  to  the  north  by  11'  33"  ;  and 
after  243  years,  wanting  43  minutes  in  a  point  more 

*  See  the  Connoissance  des  Tem{iS)  for  A.  D.  1761. 


of  the  Planets  from  the  Sun.  525 

to  the  south  by  13'  8".  But  if  the  second  conjunc- 
tion be  in  the  year  next  after  leap-year,  it  will  be  a 
day  lat»T. 

The  intervals  of  the  conjunctions  at  the  descend- 
ing node  are  somewhat  different.  The  second  hap- 
pens iu  a  period  of  8  years,  wanting  2  days  6  hours 
55  minutes,  Venus  being  got  more  to  the  north  by 
19'  58".  After  235  years  2  days  8  hours  18  mi- 
nutes, she  is  9'  21"  more  southerly  :  only,  if  the 
first  year  be  a  bissextile,  a  day  must  be  added.  And 
after  243  years  0  days  1  hour  23  minutes,  the  con- 
junction happens  10'  37"  more  to  the  north  ;  and  a 
day  later,  when  the  first  year  was  bissextile.  It  is 
supposed  as  in  the  old  style,  that  all  the  centurial 
years  are  bissextiles. 

Hence,  Dr.  Halley  finds  the  years  in  which  a 
transit  may  happen  at  the  ascending  node,  in  the 
month  of  November  (old  style)  to  be  these — 918, 
1161,  1396,  1631,  1639,  1874,  2109,  2117  :  and 
the  transit  in  the  month  of  May  (old  style)  at  the 
descending  node,  to  be  in  these  years — 1048,  1283, 
1518,  1526,  1761,  1769,  1996,  2004. 

In  the  first  case,  Dr.  HALLEY  makes  the  visible 
inclination  of  Venus's  orbit  to  be  9°  5',  and  her  ho- 
rary motion  on  the  Sun  4'  7".  In  the  latter,  he 
finds  her  visible  inclination  to  be  8'  28",  and  her 
horary  motion  4'  0".  In  either  case,  the  greatest 
possible  duration  of  a  transit  is  7  hours  56  minutes. 

Dr.  HALLEY  could  even  then  conclude,  that  if 
the  interval  in  time  between  the  two  interior  contacts 
of  Venus  with  the  Sun  could  be  measured  to  the  ex- 
actness of  a  second,  in  two  places  properly  situate, 
the  Sun's  parallax  might  be  determined  within  its 
500dth  part. — But  several  years  after,  he  explained 
this  affair  more  fully,  in  a  paper  concerning  the  tran- 
sit of  Venus  in  the  year  1761  ;  which  was  publish- 
ed in  the  Philosophical  Transactions,  and  of  which 
the  third  of  the  preceding  articles  is  a  translation ; 
the  original  having  been  written  in  J.*atm  by  the? 
Doctor, 


526  The  Method  of  finding  the  Distances 


ARTICLE  VIIL 

Containing  a  short  account  of  some  observations  of 
the  transit  oj  Venus,  A.  D.  1761,  June  6th,,  new 
style  ;  and  the  distances  of  the  planets  from  the 
Sun,  as  deduced  from  those  observations. 

Early  in  the  morning,  when  every  astronomer  was 
prepared  for  observing  the  transit,  it  unluckily  hap- 
pened, that  both  at  London  and  the  Royal  Observa- 
tory at  Greenwich,  the  sky  was  so  overcast  with 
clouds,  as  to  render  it  doubtful  whether  any  part  of 
the  transit  should  be  seen  : — and  it  was  38  minutes 
21  seconds  past  7  o'clock  (apparent  time)  at  Green- 
wich, when  the  Rev.  Mr.  Bliss,  our  Astronomer  Roy- 
al, first  saw  Venus  on  tht  Sun  ;  at  which  instant,  the 
centre  of  Venus  preceded  the  Sun's  centre  by  6'  18",  9 
of  right  ascension,  and  was  south  of  the  Sun's  cen- 
tre by  IT  42".  1  of  declination. — From  that  time  to 
the  beginning  of  egress,  the  Doctor  rmide  several  ob- 
servations, both  of  the  difference  of  right  ascension 
and  declination  of  the  centres  of  the  Sun  and  Ve- 
nus ;  and  at  last  found  the  beginning  of  egress,  or 
instant  of  the  internal  contact  of  Venus  with  the 
Sun's  limb,  to  be  at  8  hours  19  minutes  0  seconds 
apparent  time.  From  the  Doctor's  own  observa- 
tions, and  those  which  were  made  at  Shirburn  by  an- 
other gentleman,  he  has  computed,  that  the  mean 
time  at  Greenwich  of  the  ecliptical  conjunction  of  the 
Sun  and  Venus  was  at  51  minutes  20  seconds  after 
five  o'clock  in  the  morning  ;  that  the  place  of  the 
Sun  and  Venus  was  n  (Gemini)  15°  36'  33"  ;  and 
that  the  geocentric  latitude  of  Venus  was  9'  44". 9 
south. — Her  horary  motion  from  the  Sun  3'  57".  13 
retrograde  ; — and  the  angle  then  formed  by  the  axis 
of  the  equator,  and  the  axis  oi  the  ecliptic,  was  6° 
9'  34",  decreasing  hourly  1  minute  of  a  degree. — 
By  the  mean  of  three  good  observations,  the  dia- 
meter of  Venus  on  the  Sun  was  58". 


Of  the  Planets  from  the  Sun.  527 

Mr.  Short  made  his  observation  at  Savile-House 
in  London,  30  seconds  in  time  west  from  Greenwich, 
in  presence  of  his  Royal  Highness  the  Duke  of  York, 
accompanied  by  their  Royal  Highnesses  Prince  Wil* 
Ham,  Prince  Henry,  and  Prince  Frederick. — He 
first  saw  Venus  on  the  Sun  through  flying  clouds, 
at  46  minutes  37  seconds  after  5  o'clock ;  and  at 
6  hours  15  minutes  12  seconds  he  measured  the 
diameter  of  Venus  59".8. — He  afterward  found  it  to 
be  58". 9  when  the  sky  was  more  favourable. — And, 
through  a  reflecting  telescope  of  two  feet  focus, 
magnifying  140  times,  he  found  the  internal  contact 
of  Venus  with  die  Sun's  limb  to  be  at  8  hours  18 
minutes  21|  seconds,  apparent  time;  which,  being 
reduced  to  the  apparent  time  at  Greenwich,  was  8 
hours  18  minutes  51|  seconds  :  so  that  his  time  of 
seeing  the  contact  was  8£  seconds  sooner  (in  absolute 
time)  than  the  instant  of  its  being  seen  at  Greenwich. 

Messrs.  Ellicott  and  Doland  observed  the  internal 
contact  at  Hackney,  and  their  time  of  seeing  it,  re- 
duced to  the  time  at  Greenwich,  was  at  8  hours  1 8 
minutes  36  seconds,  which  was  4  seconds  sooner  in 
absolute  time  than  the  contact  was  seen  at  Greenwich. 

Mr.  Canton,  in  Spittle- Square,  London,  4'  11" 
west  of  Greenwich  (equal  to  16  seconds  44  thirds 
of  time),  measured  the  Sun's  diameter  31'  33"  24"', 
and  the  diameter  of  Venus  on  the  Sun  58";  and  by 
observation  found  the  apparent  time  of  the  internal 
contact  of  Venus  with  the  Sun's  limb  to  be  at  8 
hours  18  minutes  41  seconds;  which,  by  reduction, 
was  only  2£  seconds  short  of  the  time  at  the  Royal 
Observatory  at  Greenwich. 

The  Reverend  Mr.  Richard  Hay  don,  at  Leskeard, 
in  Cornwall  (16  minutes  10  seconds  in  time  west 
from  London,  as  stated  by  Dr.  Bevis)  observed  the 
internal  contact  to  be  at  8  hours  0  minutes  20  se- 
conds, whicfi  by  reduction  was  8  hours  16  minutes 

3  X 


528  The  Method  of  finding  the  Distances 

30  seconds  at  Greenwich;  so  that  he  must  have  seen 
it  2  minutes  30  seconds  sooner  in  absolute  time 
than  it  was  seen  at  Greenwich — -a  difference  by 
much  too  great  to  be  occasioned  by  the  difference 
of*  parallaxes.  But  by  a  memorandum  of  Mr. 
Haydotfs  some  years  before,  it  appears  that  he  then 
supposed  his  west  longitude  to  be  near  two  minutes 
more ;  which  brings  his  time  to  agree  within  half  a 
minute  of  the  time  at  Greenwich;  to  which  the 
parallaxes  will  very  nearly  answer. 

At  Stockholm  observatory,  latitude  59°  20J'  north, 
and  longitude  1  hour  12  minutes  east  from  Green- 
wich, the  whole  of  "the  transit  was  visible ;  the  total 
ingress  was  observed  by  Mr.  Wargentin  to  be  at  3 
hours  39  minutes  23  seconds  in  the  morning,  and 
the  beginning  of  egress  at  9  hours  30  minutes  8 
seconds ;  so  that  the  whole  duration  between  the  two 
internal  contacts,  as  seen  at  that  place,  was  5  hours 
50  minutes  45  seconds. 

At  Torneo  in  Lapland  ( 1  hour  27  minutes  28  se- 
conds east  of  Paris]  Mr.  Hellant,  who  is  esteemed 
a  very  good  observer,  found  the  total  ingress  to  be 
at  4  hours  3  minutes  59  seconds ;  and  the  beginning 
of  egress  to  be  9  hours  54  minutes  8  seconds. — So 
that  the  whole  duration  between  the  two  internal 
contacts  was  5  hours  50  minutes  9  seconds. 

At  Hernosand  in  Sweden  (latitude  60°  38'  north, 
and  longitude  i  hour  2  minutes  12  seconds  east  of 
Paris),  Mr.  Girter  observed  the  total  ingress  to  be 
at  3  hours  38  minutes  26  seconds;  and  the  begin- 
ning of  egress  to  be  at  9  hours  29  minutes  21  se- 
conds.— The  duration  between  these  two  internal 
contacts  5  hours  50  minutes  56  seconds. 

Mr.  DeLa  Landc,  at  Paris,  observed  the  begin- 
ning of  egress  to  be  at  8  hours  28  minutes  26  se- 
conds apparent  time — But  Mr.  Ferner  (who  was 
then  at  Constans,  14-J-"  west  of  the  Royal  Observa- 
tory at  Paris)  observed  the  beginning  of  egress  to 
be  at  8  hours  28  minutes  29  seconds  true  time. 


of  the  Planets  from  the  Sun.  529 

The  equation,  or  difference  between  the  true  and 
apparent  time,  was  1  minute  54  seconds. — The  total 
ingress,  being  before  the  Sun  rose,  could  not  be  seen. 

At  Tobolsk  in  Siberia ,  Mr.  Chappe  observed  the 
total  ingress  to  be  at  7  hours  0  minutes  28  seconds 
in  the  morning,  and  the  beginning  of  egress  to  be  at 
49  minutes  20J  seconds  after  12  at  noon. — So  that 
the  whole  duration  of  the  transit  between  the  inter- 
nal contacts  was  5  hours  48  minutes  52^  seconds, 
as  seen  at  that  place ;  which  was  2  minutes  3|  se- 
conds less  than  as  seen  at  Hernosand  in  Sweden. 

At  Madras,  the  Reverend  Mr.  Hirst  observed 
the  total  ingress  to  be  at  7  hours  47  minutes  55  se- 
conds apparent  time  in  the  morning ;  and  the  be- 
ginning of  egress  at  1  hour  39  minutes  38  seconds 
past  noon.  The  duration  between  these  two  inter- 
nal contacts  was  5  hours  51  minutes  43  seconds. 

Professor  Mathenci  at  Bologna  observed  the  be- 
ginning of  egress  to  be  at  9  hours  4  minutes  58  se- 
conds. 

At  Calcutta  (latitude  22°  30'  north,  nearly  92° 
east  longitude  from  London)  Mr.  William  Magee 
observed  the  total  ingress  to  be  at  8  hours  20  mi- 
nutes 58  seconds  in  the  morning,  and  the  beginning 
of  egress  to  be  at  2  hours  11  minutes  34  seconds  in 
the  afternoon.  The  duration  between  the  two  inter- 
nal contacts  5  hours  50  minutes  36  seconds. 

At  the  Cape  of  Good  Hope  (1  hour  13  minutes 
35  seconds  east  from  Greenwich]  Mr.  Mason  ob- 
served the  beginning  of  egress  to  be  at  9  hours  39 
minutes  50  seconds  in  the  morning. 

All  these  times  are  collected  from  the  observers' 
accounts,  printed  in  the  Philosophical  Transactions 
for  the  year  1762  and  1763,  in  which  there  are  se- 
veral other  accounts  that  I  have  not  transcribed. — 
The  instants  of  Venus's  total  exit  from  the  Sun  are 
likewise  mentioned ;  but  they  are  here  left  out,  as 
not  of  any  use  for  finding  the  Sun's  parallax. 


530  The  Method  of  finding  the  Distances 

Whoever  compares  these  times  of  the  internal 
contacts,  as  given  in  by  different  observers,  will  find 
such  difference  among  them,  even  those  which  were 
taken  upon  the  same  spot,  as  will  shew,  that  the  in- 
stant of  either  contact  could  not  be  so  accurately 
perceived  by  the  observers  as  Dr.  HAL  LEY  thought 
it  could ;  which  probably  arises  from  the  difference 
of  people's  eyes,  and  the  different  magnifying  pow- 
ers of  those  telescopes  through  which  the  contacts 
were  seen. — If  all  the  observers  had  made  use  of 
equal  magnifying  powers,  there  can  be  no  doubt 
but  that  the  times  would  have  more  nearly  coin- 
cided; since  it  is  plain,  that  supposing  all  their  eyes 
to  be  equally  quick  and  good,  they  whose  telescopes 
magnified  most,  would  perceive  the  point  of  inter- 
nal contact  soonest,  and  of  the  total  exit  latest. 

Mr.  Short  has  taken  an  incredible  deal  of  pains 
in  deducing  the  quantity  of  the  Sun's  parallax,  from 
the  best  of  those  observations  which  were  made  both 
in  Britain  and  abroad :  and  finds  it  to  have  been 
8".  52  on  the  day  of  the  transit,  when  the  Sun  was 
very  nearly  at  his  greatest  distance  from  the  Earth ; 
and  consequently  8' '.65  when  the  Sun  is  at  his 
mean  distance  from  the  Earth. — And  indeed,  it 
would  be  very  well  worth  every  curious  person's 
while  to  purchase  the  second  part  of  Volume  LII. 
of  the  Philosophical  Transactions  for  the  year  1763; 
even  if  it  contained  nothing  more  than  Mr.  Short's 
paper  on  that  subject. 

The  log.  sine  (or  tangent)  of  8". 65  is  5.6219140, 
which  being  subtracted  from  the  radius  10.0000000, 
leaves  remaining  the  logarithm  4.3780860,  whose 
number  is  23882. 84;  which  is  the  number  of  semi- 
diameters  of  the  Earth  that  the  Sun  is  distant  from 
it. — And  this  last  number,  23882.84,  being  multN 
plied  by  3985,  the  number  of  English  miles  con- 
tained in  the  Earth's  semidiameter,  gives  95, 173, 127 
miles  for  the  Earth's  mean  distance  from  the  Sun. — 
But  because  it  is  impossible,  from  the  nicest  obser- 


of  the  Planets  from  the  Sun.  531 

rations  of  the  Sun's  parallax,  to  be  sure  of  its  true 
distance  from  the  Earth  within  100  miles,  we  shall 
at  present,  for  the  sake  of  round  numbers,  state  the 
Earth's  mean  distance  from  the  Sun  at  95,173,000 
English  miles. 

And  then,  from  the  numbers  and  analogies  in  $  11 
and  14  of  this  Dissertation,  we  find  the  mean  dis- 
tances of  all  the  rest  of  the  planets  from  the  Sun  in 
miles  to  be  as  follows:  --Mercury 's  distance,  36,  841, 
468;  Venus's  distance,  68,891,486;  Mar's  distance, 
145,014,148;  Jupiter's  distance,  494,990,976;  and 
Saturn's  distance,  907,956,130. 

So  that  by  comparing  these  distances  with  those 
in  the  tables  at  the  end  of  the  chapter  on  the  solar 
system*,  it  will  be  found  that  the  dimensions  of  the 
system  are  much  greater  than  what  was  formerly 
imagined  :  and  consequently,  that  the  Sun  and  the 
planets  (except  the  Earth)  are  much  larger  than  as 
stated  in  that  table. 

The  semidiameter  of  the  Earth's  annual  orbit 
being  equal  to  the  Earth's  mean  distance  from  the 
Sun,  viz.  95,173,000  miles,  the  whole  diameter 
is  190,346,000  miles.  And  since  the  diameter  of 
a  circle  is  to  its  circumference  as  1  to  3. 141 59  the 
circumference  of  the  Earth's  orbit  is  597,989.090 
miles. 

And,  as  the  Earth  describes  this  orbit  in  365  days 
6  hours  (or  in  8766  hours),  it  is  plain  that  it  travels 
at  the  rate  of  68,217  miles  every  hour,  and  conse- 
quently 11,369  miles  every  minute ;  so  that  its  velo- 
city in  its  orbit  is  at  least  142  times  as  great  as  the 
velocity  of  a  cannon-ball,  supposing  the  ball  to  move 
through  8  miles  in  a  minute,  which  it  is  found  to  do 
very  nearly; — and  at  this  rate  it  would  take  22 
years  228  days  for  a  cannon-ball  to  go  from  the  , 
'Earth  to  the  Sun. 

On  the  3d  of  June,  in  the  year  1769,  Venus  will 
again  pass  over  the  Sun's  disc,  in  such  a  manner, 

*  Fronting  page  72. 


532  The  Method  of  finding  the  Instances 

as  to  afford  a  much  easier  and  better  method  of  in- 
vestigating  the  Sun's  parallax  than  her  transit  in  the 
year  1761  has  done. — But  no  part  of  Britain  will 
be  proper  for  observing  that  transit,  so  as  to  deduce 
any  thing  with  respect  to  the  Sun's  parallax  from  it, 
because  it  will  begin  but  a  little  before  sun-set,  and 
will  be  quite  over  before  2  o'clock  next  morning. — 
The  apparent  time  of  conjunction  of  the  Sun  and 
Venus,  according  to  Dr.  H  ALLEY'S  tables,  will  be 
at  13  minutes  past  10  o'clock  at  night  at  London; 
at  which  time  the  geocentric  latitude  of  Venus  will 
be  full  10  minutes  of  a  degree  north  from  the  Sun's 
centre  :— and  therefore,  as  seen  from  the  northern 
parts  of  the  Earth,  Venus  will  be  considerably  de- 
pressed by  a  parallax  of  latitude  on  the  Sun's  disc ; 
on  which  account,  the  visible  duration  of  the  transit 
will  be  lengthened ;  and  in  the  southern  parts  of  the 
Earth  she  will  be  elevated  by  a  parallax  of  latitude 
on  the  Sun,  which  will  shorten  the  visible  duration 
of  the  transit,  with  respect  to  its  duration  as  sup- 
posed to  be  seen  from  the  Earth's  centre ;  to  both 
which  affections  of  duration  the  parallaxes  of  longi- 
tude will  also  conspire. — So  that  every  advantage 
which  Dr.  H  ALLEY  expected  from  the  late  transit 
will  -be  found  in  this,  without  the  least  difficulty  or 
embarrassment. — It  is  therefore  to  be  hoped,  that 
neither  cost  nor  labour  will  be  spared  in  duly  ob- 
serving this  transit ;  especially  as  there  will  not  be 
such  another  opportunity  again  in  less  than  105  years 
afterward. 

The  most  proper  places  for  observing  the  transit, 
in  the  year  1769,  is  in  the  northern  parts  of  Lap- 
land and  the  Solomon  Isles  in  the  great  South-  Sea  ; 
at  the  former  of  which,  the  visible  duration  between 
the  two  internal  contacts  will  be  at  least  22  minutes 
greater  than  at  the  latter,  even  though  the  Sun's  pa- 
rallax should  not  be  quite  9"- If  it  be  9"  (which 

is  the  quantity  I  had  assumed  in  a  delineation  of  this 


of  the  Planets  from  the  Sun.  .  533 

transit,  which  I  gave  in  to  the  Royal  Society  before 
I  had  heard  what  Mr.  Short  had  made  it  from  the 
observations  on  the  late  transit),  the  difference  of 
the  visible  durations,  as  seen  in  Lapland  and  in  the 
Solomon  Isles>  will  be  as  expressed  in  that  delinea- 
tion ;  and  if  the  Sun's  parallax  be  less  than  9"  (as  I 
now  have  very  good  reason  to  believe  it  is),  the 
difference  of  durations  will  be  less  accordingly. 


INDEX, 


The  numeral  Figures  refer  to  the  Pages,  and  the 
small  n  to  the  Notes  subjoined. 

A. 

e  stars,  160. 
jEras  or  epochs,  421. 

Angle,  under  which  an  object  appears,  what,  128,  n, 
Annual  parallax  of  the  stars,  138. 
Anomaly,  what,  176. 
Ancients,  their  superstitious  notions  of  eclipses,  303* 

Their  method  of  dividing  the  zodiac >  381. 
Antipodes')  what,  86. 
Apsides,  line  of,  176. 

ARCHIMEDES,  his  ideal  problem  for  moving  the  Earth,  i  12, 
Areas,  described  by  the  planets,  proportional  to  the  times? 

109. 
Astronomy,  the  great  advantages  arising  from  it  both  in  out: 

religious  and  civil  concerns,  3 1 . 
Discovers  the  laws  by  which  the  planets  move,  antt  are 

retained  in  their  orbits,  31. 
Atmosphere,  the  higher  the  thinner,  121. 
Its  prodigious  expansion,  121. 
Its  whole  weight  on  the  Earth,  122. 
Generally  thought  to  be  heaviest  when  it  is  lightest,  123, 
Without  it,  the  heavens  would  appear  dark  in  the  day-time* 

123. 

Is  the  cause  of  twilight,  124. 
Its  height,  124. 
Refracts  the  Sun's  rays,  124. 
Causeth  the  Sun  and  Moon  to  appear  above  the  horizon 

when  they  are  really  below  it,  124. 
Foggy,  deceives  us*  in  the  bulk  and  distance  of  objectsj 

129. 

Attraction,  76. 

Decreases  as  the  square  of  the  distance  increases,  76. 
Greater  in  the  larger  than  in  the  smaller  planets,  1 12. 
Greater  in  the  Sun,  than  in  all  the  planets  if  put  together, 
112, 

3Y 


INDEX. 

Axes  of  the  planets,  what,  38. 

Their  different  positions  with  respect  to  one  another, 

83. 
Axis  of  the  Eaith,  its  parallelism,  145. 

Its  position  variable  as  seen  from  the  Sun  or  Moon,  308. 

The  phenomena,  thence  arising,  310. 

B. 

Bodies,  on  the  Earth,  lose  of  their  weight  the  nearer  they 

are  to  the  equator,  82. 
How  they  might  lose  all  their  weight,  83. 
How  they  become  visible,  117. 

C. 

Calculator  (an  instrument)  described,  437. 

Calendar,  how  to  inscribe  the  Golden  numbers  right  in  it 

for  shewing  the  days  of  new  Moons,  396. 
Cannon-ball,  its  swiftness,  68. 

In  what  times  it  would  fly  from  the  Sun  to  the  different 

planets  and  fixed  stars,  68. 
CASSIKI,  his  account  of  a  double  star  eclipaed  by  the  Moon, 

53. 

His  diagrams  of  the  paths  of  the  planets,  98. 
Catalogue  of  the  eclipses,  282. 

Of  the  constellations  and  stars,  382. 
Of  remarkable  seras  and  events,  421. 
Celestial  globe  improved,  447. 

Centripetal  and  centrifugal  forces,  how  they  alternately  over- 
come each  other  in  the  motions  of  the  planets,  108,  1 1Q. 
Changes  in  the  heavens,  385. 

Circles,  of  perpetual  apparition  and  occultation,  9 1 . 
Of  the  sphere,  140. 

Contain  360  degrees  whether  they  be  great  or  small,  152. 
CPvilyear,  what,  389. 
COLUMBUS  (CHRISTOPHER)  his  story  concerning  an  eclipse, 

303. 
Clocks  and  watches,  an  easy  method  of  knowing  whether  they 

go  true  or  false,  164. 
Why  they  seldom  agree  with  the  Sim  if  they  go  true. 

168 — 181. 
How  to  regulate  them  by  equation-tables  and  a  meridian- 

line,   166. 
Cloudy  stars,  384. 
Cometartum  (an  instrument)  described,  4,44',  . 


INDEX. 

Constellations,  ancient,  their  number,  380. 
The  number  of  stars  in  each,  according  to  different  as- 
tronomers, 382. 
Cycle,  solar,  lunar,  and  Raman,  395. 

D. 

Darkness  at  our  SAVIOUR'S  crucifixion  supernatural,  317 — . 

416. 
Day^  natural  and  artificial,  what,  394. 

And  night)  always  equally  long  at  the  equator,  90. 
Natural,  not  completed  in  an  absolute  turn  of  the  Earth 

on  its  axis,  1 64. 
Degree,  what,  152. 
Digit,  what,  306,  n. 
Direction,  (number  of),  4 1 2. 

Distances  of  the  planets  from  the  Sun,  an  idea  of  them,  68. 
A  table  of  them,  73. 
How  found,  132  ;  and  in  the  Dissertation  on  the  transit  of 

Venus,  chap.  XXIII. 
Diurnal  and  annual  motions  of  the  earth  illustrated,  141 — 

145. 

Dominical  letter,  413. 
Double  projectile  force,  a  balance  to  a  quadruple  power  of 

gravity,  109. 
Double  star  covered  by  the  Moon,  52. 

E. 

Earth,  its  bulk  but  a  point  as  seen  from  the  Sun,  32. 
Its  diameter,  annual  period,  and  distance  from  the  Sim, 

49. 

Turns  round  its  axis,  49. 
Velocity  of  its  equatorial  parts,  49. 
Velocity  in  its  annual  orbit,  49. 
Inclination  of  its  axis,  49. 

Proof  of  its  being  globular,  or  nearly  so,  50,  261. 
Measurement  of  its  surface,  50. 

Difference  between  its  equatorial  and  polar  diameters,  59. 
Its  motion  round    the    Sun    demonstrated    by  gravity, 

77,  78,  by  Dr.   BRADLEY'S  observations,  80,  by  thq 

eclipses  of  Jupiter's  satellites,  158. 
Its  diurnal  motion  highly  probable  from  the  absurdity  that 

must  follow  upon  supposing  it  not  to  move,  78,  86,  and 

demonstrable  from  its  figure,  87,  this  motion  cajiijot  be 

felt,  83. 


INDEX, 


Objections  against  its  motion  answered,  80,  85. 

It  has  no  such  thing  as  an  upper  or  an  under  side,  86.  in 

what  case  it  might,  87. 
The  swiftness  of  its  motion  in  its  orbit  compared  with 

the  velocity  of  light,  139. 

Its  diurnal  and  annual  motions  illustrated  by  an  easy  ex- 
periment, 141. 
Proved  to  be  less  than  the  Sun,  and  bigger  than  the  Moon, 

262. 

Easter  cycle,  412. 

JLclijisarcon  (an  instrument)  described,  458. 
fclijises  of  Jupiter's  satellites,  how  the  longitude  is  found 

by  them,  154,  they  demonstrate  the  velocity  of  light; 

156. 

Of  the  Sun  and  Moon,  261 — 316. 
Why  they  happen  not  in  every  month,  263. 
When  they  must  be,  263. 
Their  limits,  264. 
Their  period,  268, 

A  Dissertation  on  their  progress,  268. 
A  large  catalogue  of  them,  282. 
Historical  ones,  30 1 . 

More  of  the  Sun  than  of  the  Moon,  and  why,  303. 
The  proper  elements  for  their  calculation  and  projection, 

318. 
gclifitiC)  its  signs,  their  names  and  characters,  68. 

Makes  different  angles  with  the  horizon  every  hour  and 

minute,  234,  how  these  angles  may  be  estimated  by  the 

position  of  the  Moon's  horns,  220. 
Its  obliquity  to  the  equator  less  now  than  it  was  formerly, 

388. 
Elongations,  of  the  planets,  as  seen  by  an  observer  at  rest  on 

the  outside  of  all  their  orbits,  94. 

Of  Mercury  and  Venus,  as  seen  from  the  Earth,  illus- 
trated, 102,  its  quantity,  102. 
Of  Mercury,  Venus,  the  Earth,  Mars,  and  Jupiter  ;  their 

quantities,  as  seen  from  Saturn,  105. 
Equation  of  time,  165—181, 
Equator,  day  and  night  always  equal  there,  90. 
Makes  always  the  same  angle  with  the  horizon  of  the 

same  place;  the  ecliptic  not,  234. 
Equinoctial  points  in  the  heavens,  their  precession,  181,s* 

very  different  thing  from  the  recession  or  anticipation 

of  the  equinoxes  on  the  Earth,  the  one  no  ways  occar 

sioned  by  the  other,  185. 
Eccentricities  of  the  planets'  orbits,  11®. 


INDEX, 


F. 

fallacies  in  judging  of  the  bulk  of  objects  by  their  apparent, 
distance,  128,  applied  to  the  solution  of  the  horizontal 
Moon,  131. 

first  meridian ,  what,  152, 

fixed  stars-)  why  they  appear  of  less  magnitude  when  view- 
ed through  a  telescope  than  by  the  bare  eye,  578. 
Their  number,  379. 
Their  division  into  different  classes  and  constellations,  38Q. 


G, 

General  phenomena  of  a  superior  planet  as  seen  from  an  in- 
ferior, 106. 
Georgium  Sidus,  its  distance,  diameter,  magnitude,  annual 

revolution,  63,  n. 

Not  readily  distinguished  from  a  fixed  star,  63,  n. 
Inclination  of  its  orbit,  63,  n. 
Place  of  its  nodes,  63,  n. 

Its  satellites,  their  distance,  periods,  and  remarkable  po- 
sition of  their  orbits,  63,  n. 
Gravity,  demonstrable,  74 — 75. 

Keeps  all  bodies  on  the  Earth  to  its  surface,  or  brings 
them  back  when  thrown  upward ;  and  constitutes  their 
weight,  74,  86. 

Retains  all  the  planets  in  their  orbits,  75. 
Decreases  as  the  square  of  the  distance  increases,  76. 
Proves  the  Earth's  annual  motion,  77. 
Demonstrated  to  be  greater  in  the  larger  planets  than  in 
the  smaller ;  and  stronger  in  the  Sun  than  in  all  the 
planets  together,  112. 
Hard  to  understand  what  it  is,  1 13. 

Acts  every  moment,  115. 
Globe  (Celestial),  improved,  447. 


H. 

Harmony  of  the  celestial  motions,  78. 
Harvest -Moon,  233 — 246. 

None  at  the  equator,  233. 

Remarkable  at  the  polar  circles,  241. 

Jn  what  years  most  and  least  advantageous,  245. 


INDEX. 

Heat,  decreases  as  the  square  of  the  distance  from  the  Sun 

increases,  118. 

Why  not  greatest  when  the  Earth  is  nearest  the  Sun,  151. 
Why  greater  about  three  o'clock  in  the  afternoon  than 

when  the  Sun  is  on  the  meridian,  252. 
Heavens,  seem  to  turn  round  with  different  velocities  as 
seen  from  the  different  planets  ;  and  on  different  axes 
as  seen  from  most  of  them,  83. 
Only  one  hemisphere  of  them  seen  at  once  from  any  one 

planet's  surface,  88. 
Changes  in  them,  385. 
Horizon,  what,  88,  n. 
Horizontal  Moon  explained,  131. 
Horizontal  parallax,  of  the  Mocin,  132;   of  the  Sun,  135; 

best  observed  at  the  equator,  137. 
Hour-circles,  what,  153. 
Hour  of  time  equal  to  15  degrees  of  motion,  153. 

How  divided  by  the  Jews,  Chaldeans,  and  Arabians,  395. 
HUYGENIUS,  his  thoughts  concerning  the  distance  of  some 
stars,  32. 


I. 

Inclination  of  Venus's  axis,  43. 
Of  the  Earth's,  49. 

Of  the  axis  or  orbit  of  a  planet  only  relative,  145. 
Inhabitants  of  the  Earth  (or  any  other  planet)  stand  on  op- 
posite sides  with  their  feet  toward  one  another,  yet  each 
thinks  himself  on  the  upper  side,  86. 


•J. 

Julian  period,  415. 

Jupiter,  its  distance,  diameter,  diurnal  and  annual  revolu- 
tions, 56,  57. 

The  phenomena  of  its  belts,  57. 
Has  no  difference  of  seasons,  58. 

Has  four  Moons,  58,  their  grand  period,   58,  the  angles 
•which  their  orbits  subtend,  as  seen  from  the  Earth,  59. 
most  of  them  are  eclipsed  in  every  revolution,  59. 
The  great  difference  between  its  equatorial  and  polar 

diameters,  59. 

The  inclination  of  its  orbit,  and  place  of  its  ascending 
node,  60. 


INDEX. 

The  Sun's  light  3000  times  as  strong  on  it  as  full  Moor 

light  is  on  the  Earth,  64. 
Is  probably  inhabited,  65. 

The  amazing  power  required  to  put  it  in  motion,  112. 
The  figures  of  the  paths  described  by  its  satellites,  228, 


L. 

Light,  the  inconceivable  smallness  of  its  particles,  116;  and 
the  great  mischief  they  would  do  if  they  were  larger, 
117. 
Its  surprising  velocity,  117,  compared  with  the  swiftness 

of  the  Earth's  annual  motion,  139. 

Decreases  as  the  square  of  the  distance  from  the  lumi- 
nous body  increases,  118. 
Is  refracted  in  passing  through  different  mediums,  119, 

120. 

Affords  a  proof  of  the  Earth's  annual  motion,  139,  158. 
In  what  time  it  comes  from  the  Sun  to  the  Earth,  156  ; 

this  explained  by  a  figure,  157. 
Limits  of  eclipses,  264. 

Line,  of  the  nodes,  what,  265  ;  has  a  retrograde  motion,  267, 
LONG  (Rev.  Dr.)  his  method  of  comparing  the  quantity  of 

the  surface  of  dry  land  with  that  of  the  sea,  50. 
LONG,  his  glass  sphere,  90. 
Longitude,  how  found,  152 — 155. 
Lucid  sfiots  in  thje  heavens,  384* 
Lunar  cycle  deficient,  396. 


M, 

Ma^ellantic  clouds,  385. 

Man,  of  a  middle  size,  how  much  pressed  by  the  weight  of 

the  atmosphere,  123 ;  why  this  pressure  is  not  felt,  123. 

Mars,  its  diameter,  period,  distance,  and  other  phenomena, 

55 — 56. 

Matter,  its  properties,  74. 
Mean  anomaly,  wrhat,  176. 
Mercury,  its  diameter,  period,  distance,  &c.  40. 
Appears  in  all  the  shapes  of  the  Moon,  40. 
When  it  will  be  seen  on  the  Sun,  41. 
The  inclination  of  its  orbit  and  place  of  its  ascending  node? 

41. 
Its  path  delineated,  93* 


INDEX. 

Experiment  to  shew  its  phases,  and  apparent  motion,  103, 
Mercury  (Quicksilver)  in  the  barometer,  why  not  affected 

by  the  Moon's  raising  tides  in  the  air,  260. 
Meridian,  first,  152. 

Line,  how  to  draw  one,  166. 
Milky  way,  what,  383.  •* 

Months,  Jewish,  Arabian,  Egyfitian,  and  Grecian^  391. 
Moon,  her  diameter  and  period,  51. 

Her  phases,  51,  218. 

Shines  not  by  her  own  light,  52. 

Has  no  difference  of  seasons,  52. 

The  Earth  is  a  Moon  to  her,  52. 

Has  no  atmosphere  of  any  visible  density,  52 ;  nor  seas, 
53. 

How  her  inhabitants  may  be  supposed  to  measure  their 
year,  55. 

Her  light  compared  with  day-light,  64. 

The  eccentricity  of  her  orbit,  73. 

Is  nearer  the  earth  now  than  she  was  formerly,  1 15. 

Appears  bigger  on  the  horizon  than  at  any  considerable 
height  above  it,  and  why,  131;  yet  is  seen  nearly  under 
the  same  angle  in  both  cases  ;  1 3 1 . 

Her  surface  mountainous,  217:   if  smooth*  she  could  give 
us  no  light,  217. 

Why  no  hills  appear  round  her  edge,  217. 

Has  no  twilight,  218. 

Appears  not  always  quite  round  when  full,  219. 

Her  phases  agreeably  represented  by  a  globular  stone 
viewed  in  sunshine  when  she  is  above  the  horizon, 
and  the  observer  placed  as  if  he  saw  her  on  the  top  of 
the  stone,  219. 

Turns  round  her  axis,  22 1 . 

The  length  of  her  solar  and  sidereal  day,  221. 

Her  periodical  and  synodical  revolution  represented  by 
the  motions  of  the  hour  and  minute  hands  of  a  watch, 
222. 

Her  path  delineated,  and  shewn  to  be  always  concave  to 
the  Sun,  223 — 227* 

Her  motion  alternately  retarded  and  accelerated,  226. 

Her  gravity  toward  the  Sun  greater  than  toward  the 
Earth  at  her  conjunction,  and  why  she  does  not  then 
abandon  the  Earth  on  that  accoimt,  227. 

Rises  nearer  the  time  of  sun-set  when  about  the  full  in 
harvest  for  a  whole  week  than  when  she  is  about  the 
full  at  any  other  time  of  the  year,  and  why,  233 — 240  : 
this  rising  goes  through  a  course  of  increasing  and  de- 
creasing benefit  to  the  farmers  every  19  years,  245. 


INDEX. 

JMbon  continues  above  the  horizon  of  the  poles  for  fourteen 

of  our  natural  days  together,  246. 
Proved  to  be  globular,  261 ;  and  to  be  less  than  the  Earth, 

262. 
Her  Nodes,  263  ;  ascending  and  descending,  267;  their 

retrograde  motion,  267. 

Her  acceleration  proved  from  ancient  eclipses,  278,  n. 
Her  apogee  and  perigee,  305. 

Not  invisible  when  she  is  totally  eclipsed,  and  why,  314. 
How  to  calculate  her  conjunctions,  oppositions,  and  eclip- 
ses, 318. 

How  to  find  her  age  in  any  lunation  by  the  Golden  num- 
ber, 452. 

Morning  and  evening  star,  what,  104. 
Motion,  naturally  rectilineal,  74. 

Apparent,  of  the  planets  as  seen  by  a  spectator  at  rest 
on  the  outside  of  all  their  orbits,  94  ;  and  of  the  hea- 
vens as  seen  from  any  planet,  95. 
Natural  day,  not  completed  in  the  time  that  the  Earth  turns 

round  its  axis,  164. 

JVeiv  and,/tt//  Moon,  to  calculate  the  times  of,  318— -328. 
JV5?w  stars,  396  ;  cannot  be  comets,  385. 
JVew  style,  its  origin,  390. 

Nodes  of  the  planets'  orbits,  their  places  in  the  ecliptic,  38. 
Of  the  Moon's  orbit,  263  ;  their  retrograde  motion,  267. 
JVbnagesimal  degree,  what,  220. 
Number  of  Direction,  4 1 2 » 


O. 

Objects,  we  often  mistake  their  bulk  by  mistaking  their  dis- 
tance, 128. 

Appear  bigger  when  seen  through  a  fog  than  through 
clear  air,  and  why,  129  ;  this  applied  to  the  solution  of 
the  horizontal  Moon,  131. 

Oblique  sphere,  what,  93. 

Olympiads,  what,  279,  n. 

Orbits  of  the  planets  not  solid,  39. 

Orreries  described,  430,  434,  437. 


P. 


Parallax,  horizontal,  what,  132. 
Parallel  sfihere,  what,  93. 

32 


INDEX. 

Path  of  the  Moon,  223—226. 

Of  Jupiter's  moons,  228. 
Pendulums,  their  vibrating  slower  at  the  equator  than  near 

the  poles  proves  that  the  Earth  turns  on  its  axis,  82. 
Penumbra  what,  305. 

Its  velocity  on  the  Earth  in  solar  eclipses,  307. 
Period  of  Edifises,  268,  282. 
Phases  of  the  Moon,  213. 

Planet s,  much  of  the  same  nature  with  the  Earth,  35. 
Some  have  Moons  belonging  to  them,  35. 
Move  all  the  same  way  as  seen  from  the  Sun,  but  not  as 

seen  from  one  another,  37. 
Their  moons  denote  them  to  be  inhabited,  66. 
Planets  the  proportional  breadth  of  the  Sun's  disc,  as  seen 

from  each  of  them,  67. 

Their  proportional  bulks  as  seen  from  the  Sun,  67. 
An  idea  of  their  distances  from  the  Sun,  68. 
Appear  bigger  and  less  by  turns,  and  why,  68. 
Are  kept  in  their  orbits  by  the  power  of  gravity,  74,  107 

—  112. 

Their  motions  very  irregular  as  seen  from  the  Earth,  97. 
The  apparent  motions  of  Mercury  and  Venus  delineated 

by  pencils  in  an.  Orrery,  98. 

Elongations  of  all  the  rest  as  seen  from  Saturn,  105. 
Describe  equal  areas  in  equal  times,  109. 
The  eccentricities  of  their  orbits,  1 10. 
In  what  times  they  would  fell  to  the  Sun  by  the  power 

of  gravity,  111. 

Disturb  one  another's  motions,  the  consequence  of  it,  1 15. 
Appear  dimmer  when  seen  through  telescopes  than  by 

the  bare  eye,  the  reason  of  this,  119. 
Planetary  globe  described,  449. 
Polar  circles,  1 40. 
Poles  of  the  planets,  what,  38. 
Of  the  world,  what,  86. 
Celestial,  seem  to  keep  in  the  same  points  of  the  heavens 

all  the  year,  and  why,  138. 
Precession  of  the  Equinoxes,  181  — 186. 
Projectile  force,  107;  if  doubled,  would  require  a  quadruple 
power  of  gravity  to  retain  the  planets  in  their  orbits, 
109. 
Is  evidently  an  impulse  from  the  hand  of  the  ALMIGHTY* 

114. 
PtolcTxcan  system  absurd,  71>  100. 


INDEX. 


R. 

Kays  of  light,  when  not  disturbed,  move  in  straight  lines, 

and  hinder  not  one  another's  motions,   1 17. 
Are  refracted  in  passing  through  different  mediums,  119. 
Reflection  of  the  atmosphere,  causes  the  twilight,  123. 
Refraction  of  the  atmosphere  bends  the  rays  of  light  from, 
straight  lines,  and  keeps  the  Sun  and  Moon  longer  in 
sight  than  they  would  otherwise  be,  124. 
A  surprising  instance  of  this,  1  7. 
Must  be  allowed  for  in  taking  the  altitudes  of  the  celes- 
tial bodies,  127.      j 
Right  sphere,  93, 


S. 


Satellites,  the  times  of  their  revolutions  round  their  prima- 
ry planets,  51,  58,  61. 

Their  orbits  compared  with  each  other,  with  the  orbits 
of  the  primary  planets,  and  with  the  Sun's  circumfer- 
ence, 231. 

What  sort  of  curves  they  describe,  231. 
Saturn,  with  his  ring  and  moons,  their  phenomena,  60 — 62W 
The  Sun's  light  1000  times  as  strong  to  Saturn  *s  the 

light  of  the  full  Moon  is  to  us,  64. 
The  Phenomena  of  his  ring  farther  explained,  149. 
Our  blessed  SAVIOUR,  the  darkness  at  his  crucifixion  super- 
natural, 317. 
The  prophetic  year  of  his  crucifixion  found  to  agree  with 

an  astronomical  calculation,  416. 
Seasons,  different,  illustrated  by  an  easy  experiment,   141  ^ 

by  a  figure,   145. 
Shadow*,  what,  261. 

Sidereal  time,  what,   1 60  ;  the  number  of  sidereal  days   in 
a  year  exceeds  the  number  of  solar  days  by  one,  and 
why,   164. 
An  easy  method  for  regulating  clocks  and  watches  by  it, 

164. 
SJIITH  (Rev.  Dr.)  his  comparison  between  moon-light  am! 

day-light,  64. 
His  demonstration  that  light  decreases  as  the  square  of 

the  distance  from  the  luminous  body  increases,   118. 
{Mr.  GEORGE)  his  Dissertation  on  the  progress  of  a  solar 

eclipse  ;  following  the  tables  at  276. 

Solar  astronomer,  the  judgment  he   might  be  supposed  to 
make  concerning  the  planets  and  stars,  95,  96, 


INDEX. 

Sjiherc,  parallel)  oblique,  and  right,  93. 

Its  circles,  140. 
Sfiring  and  neap,  tides,  253. 

Stars,  their  vast  distance  from  the  Earth,  32,  138, 
Probably  not  all  at  the  same  distance,  32. 
Shine  by  their  own  light,  and  are  therefore  Suns,   33 ; 

probably  to  other  worlds,  33. 

A  proof  that  they  do  not  move  round  the  Earth,  78. 
Have  an  apparent  slow  motion  round  the  poles  of  tht 

ecliptic,  and  why,   186. 
A  catalogue  of  them,  382. 
Cloudy,    384. 
New,  385. 

Some  of  them  change  their  places,  386.. 
Starry  heavens  have  the  same  appearance  from  any  part  o*T 

the  solar  system,  94. 

SUN,  appears  bigger  than  the  stars,  and  why,  33. 
Turns  round  -his  axis,  37. 

His  proportional  breadth  as  seen  from  the  different  plan- 
ets, 67. 
Describes  unequal  arcs  above  and  below  the  horizon  at 

different  times,  and  why,  92. 
His  centre  the  only  place  from  which  the  true  motions  of 

the  planets  could  be  seen,  95. 
Is  for  half  a  year  together  visible  at  each  pole  in  its  tum; 

and  as  long  invisible,  14),  246. 
Is  nearer  the  Earth  in  winter  than  in  summer,   151. 
Why  his  motion  agrees  so  seldom  with  the  motion  of  a 

well-regulated  clock,   165 — 181. 
Would  more  than  fill  the  Moon's  orbit,  231. 
Proved  to  be  much  bigger  than  the  Earth,  and  the  Earth 

to  be  bigger  than  the  Moon,  262. 
Systems,  the  solar,  37 — 71  ;   the  Ptolemean,  71  ;  the  Ty- 

Chonic,  72. 


T, 

Table  of  the  periods,  revolutions,  magnitudes,  distances,  cf'c. 

of  the  planets,  73. 
Of  the  air's  rarity,  compression,  and  expansion,  at  differ^ 

ent  heights,  122. 
Of  refractions,   126. 

For  converting  time  into  motion,  and  the  reverse,   159. 
For  shewing  how  much  of  the  celestial  equator  passes 

over  the  meridian  in  any  part  of  a  mean  solar  day ; 


INDEX- 

and  how  much  the  stars  accelerate  upon  tjic  meaji  solar 
time  for  a  month,  163. 
Table  of  the  first  part  of  the  equation  of  time,  171  ;  of  the 

second  part,  178. 

Of  the  precession  of  the  equinoxes,  183. 
Of  the  length  of  sidereal,  Julian,  and  tropical  years,  189. 
Of  the  Sun's  place  and  anomaly,  190 — 192. 
Of  the  equation  of  natural  days,  194 — 205. 
Of  the  equation  of  time,  208 — 216. 
Of  the  conjunctionj^*f  the  hour  and  minute  hands  pf  a 

watch,  222. 

Of  the  curves  described  by  the  satellites,  232. 
Of  the  difference  of  time  in  the  Moon's  rising  and  setting 
on  the  parallel  of  London  every  day  during  her  course 
round  the  ecliptic,  236. 
Of  the  returns  of  a  solar  eclipse^  272,  275. 
Of  eclipses,  285 — 302. 
For  calculating  new  and  full  Moons,  and  eclipses,  329— 

346. 

Of  the  constellations  and  number  of  stars,  382,  383. 
Of  the  Jewish,  Egyptian,  Arabic,  and  Grecian  months, 

392 — 394. 
For  inserting  the  Golden  numbers  right  in  the  calendar, 

397. 
Of  the  times  of  all  the  new  Moons,  for  76  years,  403 — • 

411. 

Of  remarkable  aeras  or  events,  422,  423. 
Of  the  Golden  number,  Number  of  Direction,  Dominica] 

letter,  and  days  of  the  months,  424 — 429. 
THALES'S  eclipse,  279. 
THUCYDIDES'S  eclipse,  281. 
Tides,  their  cause  and  phenomena,  249 — 260. 
Tide-Dial  described,  454. 
Trajectorium  Lunar e  described}  452*, 
Tropics*  140. 

Twilight,  none  in  the  Moon,  218, 
Tychonic  system  absurd,  72. 


17. 

Universe,  the  work  of  Almighty  Power,  Sl2,  1 14. 
Ufi  and  down,  only  relative  terms,  86. 

Or  under  side  of  the  Earth,  no  such  thing,  87 


INDEX. 


V. 

Velocity  of  Light  compared  with  the  velocity  of  the  Earth  in 

its  annual  orbit,  139. 
Venus,  her  bulk,  distance,  period,  length  of  days  and  nights, 

41. 

Is  our  morning  and  evening  star,  42. 
Her  axis,  how  situate,  43. 


The  inclination  of  her  orbit,  48. 

When  she  will  be  seen  on  the  Sun,  48. 

How  it  may  probably  be  soon  known  if  she  has  a  satel* 

lite,  48. 

Appears  in  all  the  shapes  of  the  Moon,  40,  101. 
An  experiment  to  shew  her  phases  and  apparent  motion, 

101. 
'Vision,  how  caused,  11  7. 


W. 

Weather-^  not  hottest  when  then  Sun  is  nearest  to  us,  and 

why,  151. 

Weight,  the  cause  of  it,  86. 
World,  not  eternal,  116. 


Y. 

Year,  Tropical,  Sidereal,  Lunai>  Civil,  389  ;  Bissextile; 
Roman,  390 ;  Jewish,  Egyptian,  Arabic,  and  Grecian, 
391,  394;  how  long  it  would  be  if  the  Sun  mnved 
round  the  Earth,  78. 


Z. 


Zodiac,  what,  381. 

How  divided  by  the  ancieots;  381* 
Zones,  what,  141. 


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